Heating Effect of Current and Electrical Measuring Instruments

Q 1 :
An electric bulb rated 50 W – 200 V is connected across a 100 V supply. The power dissipation of the bulb is [2024]

12.5 W
25 W
100 W
50 W

1

2

3

4

(A) Resistance, $R = \frac{V^{2}}{P} = \frac{{(200)}^{2}}{50} = 800 Ω$

Power dissipated, $P = \frac{{(V_{a p p l i e d})}^{2}}{R} = \frac{{(100)}^{2}}{800} = \frac{100}{8} = 12.5 W$

Q 2 :
The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is (Given $e = 1.6 \times 10^{- 19} C$ ) [2024]

$1.25 \times 10^{19}$
$6.25 \times 10^{17}$
$6.25 \times 10^{18}$
$31.25 \times 10^{17}$

1

2

3

4

(D) Given: P = 110 W, V = 220 V

Power, $P = V . I \Rightarrow 110 = (220) (I) \Rightarrow I = 0.5 A$

$I = \frac{q}{t} = \frac{n e}{t} \Rightarrow 0.5 = (\frac{n}{t}) \times 1.6 \times 10^{- 19}$

$(\frac{n}{t}) = \frac{0.5}{1.6 \times 10^{- 19}} = 31.25 \times 10^{17}$

Q 3 :
Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _ to times of its initial length if the water is to be boiled in 15 minutes. [2024]

increased, 4/3
increased, 3/4
decreased, 3/4
decreased, 4/3

1

2

3

4

(C) $P = \frac{V^{2}}{R}, R = \frac{ρ L}{A} \Rightarrow P = \frac{V^{2} A}{ρ L}$ or $P \propto \frac{1}{L}$

$P_{1} \times t_{1} = P_{2} \times t_{2}$

$\frac{P_{1}}{P_{2}} = \frac{t_{2}}{t_{1}} = \frac{L_{2}}{L_{1}} = \frac{15}{20} \Rightarrow L_{2} = \frac{3}{4} L_{1}$

Q 4 :
By what percentage will the illumination of the lamp decrease if the current drops by 20% ? [2024]

46%
26%
36%
56%

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2

3

4

(C) $P_{i n i t i a l} = {I^{2}}_{i n i t i a l} R$

$P_{f i n a l} = {(0.8 I_{i n i t i a l})}^{2} R$

% change in power

$\frac{P_{f i n a l} - P_{i n i t i a l}}{P_{i n i t i a l}} \times 100 = (0.64 - 1) \times 100 = - 36 %$

Q 5 :
The ratio of heat dissipated per second through the resistance $5 Ω$ and $10 Ω$ in the circuit given below is [2024]

4 : 1
1 : 1
2 : 1
1 : 2

1

2

3

4

(3)

As parallel combination so, p.d. is same $P = \frac{V^{2}}{R} \Rightarrow P \propto \frac{1}{R}$

$\frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}} = \frac{10}{5} = \frac{2}{1}$

Q 6 :
When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become [2024]

1/4 W
1/2 W
2W
4W

1

2

3

4

(4)

$W = \frac{V^{2}}{R}$ ...(1)

and $R = \frac{ρ ℓ}{A}$

Now

$R_{eq} = \frac{R}{4}$

$W' = \frac{V^{2}}{\frac{R}{4}} = \frac{4 V^{2}}{R} = 4 W$

Q 7 :
A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 Ω and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____ $Ω$ . [2024]

0%

(5)

$R_{heater} = \frac{V^{2}}{P} = \frac{{(100)}^{2}}{1000} = 10 Ω$

For heater $P = \frac{V^{2}}{R} \Rightarrow V = \sqrt{P R}$

$V = \sqrt{62.5 \times 10} = 25 V$

$i_{1} = \frac{75}{10} = 7.5 A, i_{H} = \frac{25}{10} = 2.5 A$

$i_{R} = i_{1} - i_{H} = 7.5 - 2.5 = 5 A$

$V = I R \Rightarrow R = \frac{25}{5} = 5 Ω$

Q 8 :
In the following circuit, the battery has an emf of 2V and an internal resistance of $\frac{2}{3} Ω$ . The power consumption in the entire circuit is ______ W. [2024]

0%

(3)

$R_{eq} = \frac{4}{3} Ω$

$∴ P = \frac{V^{2}}{R_{eq}} = \frac{4}{\frac{4}{3}} = 3 W$

Topic Question Set

Q 1 :
An electric bulb rated 50 W – 200 V is connected across a 100 V supply. The power dissipation of the bulb is [2024]

Q 2 :
The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is (Given $e = 1.6 \times 10^{- 19} C$ ) [2024]

Q 3 :
Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _ to times of its initial length if the water is to be boiled in 15 minutes. [2024]

Q 4 :
By what percentage will the illumination of the lamp decrease if the current drops by 20% ? [2024]

Q 5 :
The ratio of heat dissipated per second through the resistance $5 Ω$ and $10 Ω$ in the circuit given below is [2024]

Q 6 :
When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become [2024]

Q 7 :
A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 Ω and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____ $Ω$ . [2024]

0%

Q 8 :
In the following circuit, the battery has an emf of 2V and an internal resistance of $\frac{2}{3} Ω$ . The power consumption in the entire circuit is ______ W. [2024]

0%

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Topic Question Set

Q 1 : An electric bulb rated 50 W – 200 V is connected across a 100 V supply. The power dissipation of the bulb is [2024]

Q 2 : The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is (Given e=1.6×10-19C) [2024]

Q 3 : Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _________ to ________ times of its initial length if the water is to be boiled in 15 minutes. [2024]

Q 4 : By what percentage will the illumination of the lamp decrease if the current drops by 20% ? [2024]

Q 5 : The ratio of heat dissipated per second through the resistance 5Ω and 10Ω in the circuit given below is [2024]

Q 6 : When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become [2024]

Q 7 : A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 Ω and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____ Ω. [2024]

0%

Q 8 : In the following circuit, the battery has an emf of 2V and an internal resistance of 23Ω. The power consumption in the entire circuit is ______ W. [2024]

0%

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Q 1 :
An electric bulb rated 50 W – 200 V is connected across a 100 V supply. The power dissipation of the bulb is [2024]

Q 2 :
The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is (Given $e = 1.6 \times 10^{- 19} C$ ) [2024]

Q 3 :
Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _ to times of its initial length if the water is to be boiled in 15 minutes. [2024]

Q 4 :
By what percentage will the illumination of the lamp decrease if the current drops by 20% ? [2024]

Q 5 :
The ratio of heat dissipated per second through the resistance $5 Ω$ and $10 Ω$ in the circuit given below is [2024]

Q 6 :
When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become [2024]

Q 7 :
A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 Ω and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____ $Ω$ . [2024]

Q 8 :
In the following circuit, the battery has an emf of 2V and an internal resistance of $\frac{2}{3} Ω$ . The power consumption in the entire circuit is ______ W. [2024]