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If power dissipated in the 9 $\Omega$ resistor in the circuit shown is 36 watt, the potential difference across the 2 $\Omega$ resistor is
A
2 volt
B
4 volt
C
8 volt
D
10 volt
Detailed Solution
In the circuit the 9 $\Omega$ and 6 $\Omega$ resistors are in parallel, and this combination is in series with the 2 $\Omega$ resistor.
Power in the 9 $\Omega$ resistor: $P = I_1^2R$, so $36 = I_1^2\times9$, giving $I_1 = 2$ A
Potential difference across the 9 $\Omega$ resistor = $I_1R = 2\times9 = 18$ V
The same 18 V is across the 6 $\Omega$ resistor, so $I_2 = \frac{18}{6} = 3$ A
Total current through the 2 $\Omega$ resistor = $I_1 + I_2 = 2 + 3 = 5$ A
Potential difference across the 2 $\Omega$ resistor = $5\times2 = 10$ V
Power in the 9 $\Omega$ resistor: $P = I_1^2R$, so $36 = I_1^2\times9$, giving $I_1 = 2$ A
Potential difference across the 9 $\Omega$ resistor = $I_1R = 2\times9 = 18$ V
The same 18 V is across the 6 $\Omega$ resistor, so $I_2 = \frac{18}{6} = 3$ A
Total current through the 2 $\Omega$ resistor = $I_1 + I_2 = 2 + 3 = 5$ A
Potential difference across the 2 $\Omega$ resistor = $5\times2 = 10$ V