First slide

Electrical power

Question

What should be the value of resistance R in the circuit shown in figure so that the electric lamp consumes the rated power?

Moderate

A

$4.5 Ω$
B

$6 Ω$
C

$12 Ω$
D

None of these

Solution

The electric lamp consumes the rated power if the voltage across electric lamp is 3 V.
$∴ resistance across AB is 4 .5 Ω$
Resistance of lamp, $R_{b} = \frac{V^{2}}{P_{b}} = \frac{3^{2}}{0 .5} = 18 Ω$
$\frac{{RR}_{b}}{R_{b}} = 4 .5 Ω; 18 R = \frac{9}{2} (18 + R) \Rightarrow R = 6 Ω$

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