First slide

Electrical power

Question

If two bulbs of wattage 25 and 100 respectively each rated at 220 volt are connected in series with the supply of 440 volt, which bulb will fuse ?

Moderate

A

100 watt bulb
B

25 watt bulb
C

none of them
D

both of them

Solution

Resistance of 25 watt bulb
$R_{1} = \frac{V^{2}}{P} = \frac{(220)^{2}}{25} = 1936 Ω$
Resistance of 100 watt bulb
$R_{2} = \frac{V^{2}}{P} = \frac{(220)^{2}}{100} = 484 Ω$
Series resistance, $R = R_{1} + R_{2} = 2420 Ω$
Current through series combination
$i = \frac{(440)}{2420} = \frac{2}{11}$
Potential difference across 25 watt bulb
$V_{1} = R_{1} \times i = 1936 \times (2 / 11) = 352 volt$
Potential difference across 100 watt bulb
$V_{2} = R_{2} \times i = 484 \times (2 / 11) = 88 volt$
Thus the bulb of 25 watt will be fused because it can tolerate only 220 V while the voltage across it is 352 volt

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