Question 247 of 380

An electric bulb rated as $200W$ at $100V$ is used in a circuit having $200V$ supply. The resistance $R$ that must be put in series with the bulb so that the bulb delivers the same power is ______ $\Omega$.

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Answer: 50

Power, $P=\dfrac{{V}^{2}}{{R}_{B}}$
${R}_{B}=\dfrac{{V}^{2}}{P}=\dfrac{100\times 100}{200}$
${R}_{B}=50\Omega$

To produce same power, same voltage (i.e., $100V$) should be across the bulb.
Hence, $R={R}_{B}$
$R=50\Omega$