Question

The resistance of a heater coil is $110ohm$. A resistance $R$ is connected in parallel with it and the combination is joined in series with a resistance of $11ohm$ to a $220volt$ main line. The heater operates with a power of $110watt$. The value of $R$ in ohm is

• A. 12.22
• B. 24.42
• C. Negative
• D. That the given values are not correct

Answer 1

Answer: (A)

Power consumed by heater is $110W$, so by using $P=\frac{V^2}{R}$

$110=\frac{V^2}{110}$
$\Rightarrow V=110V$.
Also from figure $i_1=\frac{110}{110}=1A$
and $i=\frac{110}{11}=10A.$
So $i_2=10-1=9A$
Applying Ohm's law for resistance
$R,V=iR$
$\Rightarrow 110=9\times R$
$\Rightarrow R=12.22\Omega$