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

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(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]

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

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(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

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(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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(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

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

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]

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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]

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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]