question_answer

The resistance of a heater coil is 110 ohm. A resistance R is connected in parallel with it and the combination is joined in series with a resistance of 11 ohm to a 220 volt main line. The heater operates with a power of 110 watt. The value of R in ohm is                                                       [ISM Dhanbad 1994]

A)                    12.22

B)                    24.42                                

C)                    Negative                                

D)                    That the given values are not correct

Correct Answer: A

Solution :

           Power consumed by heater is 110 W so by using \[P=\frac{{{V}^{2}}}{R}\] \[110=\frac{{{V}^{2}}}{110}\,\,\Rightarrow \,V=110\,V.\] Also from figure \[{{i}_{1}}=\frac{110}{110}=1A\] and \[i=\frac{110}{11}=10\,A.\] So \[{{i}_{2}}=10-1=9\,A\] Applying Ohms law for resistance R, V = iR \[\Rightarrow \,\,110=9\times R\]Þ \[R=12.22\,\Omega \]