Question

A $30\,V-90\,W$ lamp is operated on a $120\,V$ DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is

• A. 10 $\Omega$
• B. 30 $\Omega$
• C. 20 $\Omega$
• D. 40 $\Omega$

Answer 1

Answer: (B)

30 $\Omega$

Answer 2

The resistance of lamp is given by
$R_{0} = \frac{V^{2}}{P} = \frac{\left(30\right)^{2}}{90} = 10\,\Omega$
The current in the lamp will be
$I = \frac{V}{R_{0} } = \frac{30}{10} = 3A$
As the lamp is operated on 120V DC, then resistance becomes
$R' = \frac{V'}{i} = \frac{120}{3} = 40 \Omega$
For proper glow, a resistance R is put in series with the bulb so that
$R' = R + R_{0}$
$\Rightarrow R^{\alpha} = R' - R_{0} = 40 - 10 = 30 \,\Omega$