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Electricity - Q&A

1. A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio R/R' is
(a) 1/25
(b) 1/5
(c) 5
(d) 25

Answer: (d) 25
Explanation:
1. Resistance is proportional to length. If a wire of resistance R is cut into 5 equal parts, each part will have a resistance of R/5.
2. When these 5 parts (each of resistance r = R/5) are connected in parallel, the equivalent resistance R' is given by:
1/R' = 1/r + 1/r + 1/r + 1/r + 1/r = 5/r
1/R' = 5 / (R/5) = 25 / R
R' = R / 25
3. The ratio R/R' = R / (R/25) = 25.

[Image of parallel resistors circuit]

2. Which of the following terms does not represent electrical power in a circuit?
(a) I2R
(b) IR2
(c) VI
(d) V2/R

Answer: (b) IR2
Explanation:
- Power (P) = VI (Option c)
- Using Ohm's Law (V = IR), substitute V in the first equation: P = (IR)I = I2R (Option a)
- Using Ohm's Law (I = V/R), substitute I in the first equation: P = V(V/R) = V2/R (Option d)
- Therefore, IR2 is the only term that does NOT represent electrical power.

3. An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be
(a) 100 W
(b) 75 W
(c) 50 W
(d) 25 W

Answer: (d) 25 W
Explanation:
1. First, find the resistance (R) of the bulb using its rating. P = V2/R → R = V2/P
R = (220)2 / 100 = 48400 / 100 = 484 Ω.
2. Now, calculate the power consumed (P') when operated at 110 V using this resistance.
P' = (V')2 / R
P' = (110)2 / 484 = 12100 / 484 = 25 W.

4. Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series to parallel combinations would be
(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1

Answer: (c) 1:4
Explanation:
Let the resistance of each wire be R.
1. Series: Equivalent resistance Rs = R + R = 2R.
Heat produced (Hs) = V2/Rs * t = (V2/2R) * t
2. Parallel: Equivalent resistance Rp = 1/R + 1/R = 2/R → Rp = R/2.
Heat produced (Hp) = V2/Rp * t = (V2/(R/2)) * t = (2V2/R) * t
3. Ratio Hs / Hp:
(V2/2R) / (2V2/R) = 1/4
So, the ratio is 1:4.

5. How is a voltmeter connected in the circuit to measure the potential difference between two points?

Answer: A voltmeter is always connected in parallel across the two points between which the potential difference is to be measured. This is because a voltmeter has very high resistance, so it draws negligible current from the circuit.

[Image of voltmeter connected in parallel]

6. A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10−8 Ω m. What will be the length of this wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?

Answer:
Part 1: Find Length
Given: Diameter (d) = 0.5 mm = 5 × 10-4 m; Radius (r) = 2.5 × 10-4 m
Resistivity (ρ) = 1.6 × 10-8 Ω m
Resistance (R) = 10 Ω
Area (A) = πr2 = 3.14 × (2.5 × 10-4)2 = 1.9625 × 10-7 m2
Formula: R = ρL/A → L = RA/ρ
L = (10 × 1.9625 × 10-7) / (1.6 × 10-8)
L = 122.7 m (approx)

Part 2: If Diameter is Doubled
Resistance is inversely proportional to the square of the diameter (R ∝ 1/d2).
If diameter is doubled (2d), the new resistance will be 1/(2)2 = 1/4 times the original.
New Resistance = 10 / 4 = 2.5 Ω.

7. The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below -
I (amperes) 0.5 1.0 2.0 3.0 4.0
V (volts) 1.6 3.4 6.7 10.2 13.2
Plot a graph between V and I and calculate the resistance of that resistor.

Answer:
To find resistance, we can take the slope of the V-I graph or calculate the average ratio V/I.
R = (V2 - V1) / (I2 - I1)
Let's take two points: (V=3.4, I=1.0) and (V=10.2, I=3.0)
R = (10.2 - 3.4) / (3.0 - 1.0)
R = 6.8 / 2.0 = 3.4 Ω
(The average resistance is approximately 3.3 to 3.4 Ω).

8. When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.

Answer:
Given: V = 12 V
I = 2.5 mA = 2.5 × 10-3 A
Formula: R = V / I
R = 12 / (2.5 × 10-3)
R = (12 × 1000) / 2.5
R = 12000 / 2.5 = 4800 Ω (or 4.8 kΩ).

9. A battery of 9 V is connected in series with resistors of 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5 Ω and 12 Ω, respectively. How much current would flow through the 12 Ω resistor?

Answer:
1. Total Resistance: Since they are in series, add all resistances.
Rtotal = 0.2 + 0.3 + 0.4 + 0.5 + 12 = 13.4 Ω
2. Total Current: I = V / Rtotal
I = 9 / 13.4 = 0.67 A (approx).
3. Current in 12 Ω Resistor: In a series circuit, the current is the same through every resistor.
So, current through 12 Ω resistor = 0.67 A.

10. How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?

Answer:
1. Required Resistance: Find the total resistance (Req) needed for the circuit.
Req = V / I = 220 / 5 = 44 Ω.
2. Number of Resistors (n): When 'n' identical resistors (R) are in parallel, the equivalent resistance is R/n.
44 = 176 / n
n = 176 / 44 = 4
So, 4 resistors are required.

11. Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of (i) 9 Ω, (ii) 4 Ω.

Answer:
(i) For 9 Ω: Connect two resistors in parallel, and the third in series with them.
- Parallel part: (6 × 6) / (6 + 6) = 36 / 12 = 3 Ω.
- Total: 3 Ω + 6 Ω (Series) = 9 Ω.

(ii) For 4 Ω: Connect two resistors in series, and the third in parallel with this combination.
- Series part: 6 + 6 = 12 Ω.
- Parallel part: (12 × 6) / (12 + 6) = 72 / 18 = 4 Ω.

12. Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?

Answer:
1. Current per bulb (I1): P = VI → I = P/V
I1 = 10 / 220 = 1/22 A.
2. Total Current allowed (Itotal): 5 A.
3. Number of bulbs (n):
n × I1 = Itotal
n × (1/22) = 5
n = 5 × 22 = 110 bulbs.

13. A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?

Answer:
V = 220 V, R = 24 Ω
Case 1: Separately (Only one coil used)
I = V / R = 220 / 24 = 9.16 A

Case 2: In Series
Req = 24 + 24 = 48 Ω
I = 220 / 48 = 4.58 A

Case 3: In Parallel
Req = 24 / 2 = 12 Ω
I = 220 / 12 = 18.33 A

14. Compare the power used in the 2 Ω resistor in each of the following circuits: (i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

Answer:
(i) Circuit 1 (Series):
Total R = 1 + 2 = 3 Ω.
Current I = V/R = 6/3 = 2 A.
Power in 2 Ω resistor (P = I2R) = (2)2 × 2 = 4 × 2 = 8 W.

(ii) Circuit 2 (Parallel):
In parallel, voltage across each resistor is same as source voltage.
Voltage across 2 Ω resistor = 4 V.
Power in 2 Ω resistor (P = V2/R) = (4)2 / 2 = 16 / 2 = 8 W.

Result: The power used is the same (8 W) in both cases.

15. Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?

Answer:
1. Current drawn by 100 W lamp (I1): I = P/V = 100/220 = 0.45 A.
2. Current drawn by 60 W lamp (I2): I = P/V = 60/220 = 0.27 A.
3. Total Current: In parallel, currents add up.
Total I = I1 + I2 = 0.45 + 0.27 = 0.72 A (approx 0.73 A if fractions kept).

16. Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?

Answer:
Energy (E) = Power × Time
TV Set:
P = 250 W, t = 1 hr = 3600 s.
E = 250 × 3600 = 9,00,000 J (or 250 Wh).
Toaster:
P = 1200 W, t = 10 min = 600 s (or 10/60 hr).
E = 1200 × 600 = 7,20,000 J (or 200 Wh).
Conclusion: The 250 W TV set uses more energy.

17. An electric heater of resistance 8 Ω draws 15 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater.

Answer:
The "rate at which heat is developed" is simply Power.
Formula: P = I2R
P = (15)2 × 8
P = 225 × 8
P = 1800 W (or 1800 J/s).

18. Explain the following.
(a) Why is the tungsten used almost exclusively for filament of electric lamps?
(b) Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?
(c) Why is the series arrangement not used for domestic circuits?
(d) How does the resistance of a wire vary with its area of cross-section?
(e) Why are copper and aluminium wires usually employed for electricity transmission?

Answer:
(a) Tungsten has a very high melting point (3380 °C) and does not oxidize (burn) easily at high temperatures. This allows it to get very hot and emit light without melting.
(b) Alloys (like nichrome) have higher resistivity than pure metals and do not oxidize easily at high temperatures. This makes them efficient at producing heat and durable.
(c) In a series circuit:
1. If one appliance fails, the circuit is broken and none work.
2. The voltage is divided, so appliances don't get the full 220 V.
3. You cannot turn appliances on/off individually.
(d) Resistance is inversely proportional to the area of cross-section (R ∝ 1/A). A thicker wire (larger area) has less resistance, and a thinner wire has more resistance.
(e) Copper and aluminium are good conductors of electricity (low resistivity). They are also relatively cheaper and ductile (can be drawn into wires) compared to other good conductors like silver.

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Quick Review Flashcards - Click to flip and test your knowledge!
Question
What constitutes an electric current in a metallic conductor?
Answer
The flow of electric charges, specifically electrons.
Question
How is the magnitude of electric current ($I$) expressed mathematically?
Answer
$I = \frac{Q}{t}$, where $Q$ is the net charge and $t$ is time.
Question
What is the SI unit of electric charge?
Answer
The coulomb ($C$).
Question
How many electrons approximately constitute one coulomb of charge?
Answer
$6 \times 10^{18}$ electrons.
Question
What is the specific negative charge possessed by a single electron?
Answer
$1.6 \times 10^{-19} C$.
Question
What is the SI unit of electric current?
Answer
The ampere ($A$).
Question
Define the unit 'ampere' in terms of charge and time.
Answer
One ampere is the flow of one coulomb of charge per second ($1 A = 1 C / 1 s$).
Question
What is the conversion factor for one milliampere ($1 mA$) to amperes?
Answer
$10^{-3} A$.
Question
What is the conversion factor for one microampere ($1 \mu A$) to amperes?
Answer
$10^{-6} A$.
Question
What term describes a continuous and closed path of an electric current?
Answer
An electric circuit.
Question
In an electric circuit, what is the convention for the direction of electric current?
Answer
The direction is taken as opposite to the direction of the flow of electrons.
Question
Which instrument is used to measure electric current in a circuit?
Answer
An ammeter.
Question
How must an ammeter be connected in a circuit to measure the current?
Answer
It must always be connected in series.
Question
In a schematic diagram, current flows from which terminal of the cell to the other?
Answer
From the positive terminal to the negative terminal.
Question
What is the function of a switch in an electric circuit?
Answer
It provides a conducting link between the cell and the bulb (or other components).
Question
What physical condition is required for electrons to move through a conducting metallic wire?
Answer
A difference of electric pressure, known as potential difference.
Question
Define electric potential difference ($V$) between two points.
Answer
$V = \frac{W}{Q}$, representing the work done ($W$) to move a unit charge ($Q$) from one point to the other.
Question
What is the SI unit of electric potential difference?
Answer
The volt ($V$).
Question
Define the 'volt' in terms of joules and coulombs.
Answer
One volt is the potential difference when $1$ joule of work is done to move a charge of $1$ coulomb.
Question
Which instrument is used to measure the electric potential difference between two points?
Answer
A voltmeter.
Question
How is a voltmeter connected in a circuit relative to the points being measured?
Answer
It is always connected in parallel.
Question
What component in a circuit is used to generate and maintain a potential difference?
Answer
A cell or a battery (combination of cells).
Question
State Ohm's Law regarding the relationship between potential difference ($V$) and current ($I$).
Answer
The potential difference across a metallic wire is directly proportional to the current flowing through it, provided temperature remains constant.
Question
Mathematically, how is resistance ($R$) defined according to Ohm's Law?
Answer
$R = \frac{V}{I}$.
Question
What is the SI unit of electrical resistance?
Answer
The ohm ($\Omega$).
Question
Define $1$ ohm of resistance in terms of voltage and current.
Answer
The resistance of a conductor when a potential difference of $1 V$ causes a current of $1 A$ to flow.
Question
How does the current through a resistor change if the resistance is doubled while voltage stays constant?
Answer
The current gets halved.
Question
What is the purpose of a rheostat in an electric circuit?
Answer
To change the resistance in the circuit and thereby regulate the current without changing the voltage source.
Question
What is the physical cause of resistance in a conductor?
Answer
The motion of electrons is retarded by the attraction of the atoms within the conductor.
Question
Define a 'good conductor' in terms of electrical resistance.
Answer
A component of a given size that offers very low resistance to the flow of current.
Question
How does the resistance of an insulator compare to that of a conductor of the same size?
Answer
An insulator offers a much higher resistance.
Question
Identify the three primary factors on which the resistance of a uniform metallic conductor depends.
Answer
Length ($l$), area of cross-section ($A$), and the nature of its material.
Question
State the relationship between the length ($l$) of a conductor and its resistance ($R$).
Answer
Resistance is directly proportional to length ($R \propto l$).
Question
State the relationship between the cross-sectional area ($A$) of a conductor and its resistance ($R$).
Answer
Resistance is inversely proportional to the area of cross-section ($R \propto \frac{1}{A}$).
Question
What is the formula for resistance ($R$) including resistivity ($\rho$)?
Answer
$R = \rho \frac{l}{A}$.
Question
What does the constant $\rho$ (rho) represent in the resistance formula?
Answer
Electrical resistivity, a characteristic property of the material.
Question
What is the SI unit of electrical resistivity?
Answer
The ohm metre ($\Omega m$).
Question
Compare the resistivity levels of metals/alloys versus insulators.
Answer
Metals/alloys have very low resistivity ($10^{-8}$ to $10^{-6} \Omega m$), while insulators have very high resistivity ($10^{12}$ to $10^{17} \Omega m$).
Question
How does the resistivity of an alloy generally compare to its constituent metals?
Answer
The resistivity of an alloy is generally higher than that of its constituent metals.
Question
Why are alloys like nichrome commonly used in electrical heating devices?
Answer
They have high resistivity and do not oxidise (burn) readily at high temperatures.
Question
Which metal is used almost exclusively for the filaments of electric bulbs due to its high melting point?
Answer
Tungsten.
Question
Which two metals are commonly used for electrical transmission lines due to their low resistivity?
Answer
Copper and aluminium.
Question
When resistors are connected in series, how does the current through each resistor compare?
Answer
The current is the same in every part of the circuit and through each resistor.
Question
How is the total potential difference ($V$) distributed across resistors connected in series?
Answer
It is equal to the sum of the potential differences across the individual resistors ($V = V_1 + V_2 + V_3$).
Question
What is the formula for the equivalent resistance ($R_s$) of resistors joined in series?
Answer
$R_s = R_1 + R_2 + R_3 + \dots$
Question
Is the equivalent resistance of a series combination larger or smaller than any individual resistance in the set?
Answer
Larger.
Question
When resistors are connected in parallel, how does the potential difference across each resistor compare?
Answer
The potential difference across each resistor is the same and equal to the total potential difference.
Question
How is the total current ($I$) distributed in a parallel combination of resistors?
Answer
The total current is the sum of the separate currents through each branch ($I = I_1 + I_2 + I_3$).
Question
What is the formula for the reciprocal of the equivalent resistance ($R_p$) in a parallel circuit?
Answer
$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$
Question
What is a major disadvantage of connecting household appliances in series?
Answer
If one component fails, the circuit is broken and all other components stop working.
Question
Why is it impractical to connect an electric bulb and an electric heater in series?
Answer
They require widely different values of current to operate properly.
Question
What happens to the source energy in a purely resistive electric circuit?
Answer
The energy gets dissipated entirely in the form of heat.
Question
What is the mathematical expression for Joule’s Law of heating?
Answer
$H = I^2 Rt$.
Question
According to Joule's Law, how is the heat produced ($H$) related to the current ($I$)?
Answer
Heat produced is directly proportional to the square of the current ($H \propto I^2$).
Question
Why are electric bulbs filled with chemically inactive gases like nitrogen and argon?
Answer
To prolong the life of the filament by preventing oxidation.
Question
What is the function of a fuse in an electric circuit?
Answer
It protects circuits and appliances by melting and breaking the circuit if the current exceeds a specified value.
Question
How is a fuse wire connected relative to the device it protects?
Answer
It is connected in series with the device.
Question
Define electric power ($P$).
Answer
The rate at which electric energy is dissipated or consumed in an electric circuit ($P = VI$).
Question
What is the SI unit of electric power?
Answer
The watt ($W$).
Question
Express $1$ watt in terms of volts and amperes.
Answer
$1 W = 1 V \times 1 A$.