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

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

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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