In which of the following circuit maximum power dissipation is observed (power)

Question

Accepted Answer

The correct option is (1):

In an AC circuit, the power dissipated is given by the formula $P_{avg} = V_{rms} 	imes I_{rms} 	imes \cos(\phi)$, where $V_{rms}$ is the root mean square voltage, $I_{rms}$ is the root mean square current, and $\phi$ is the phase angle between the voltage and current. The term $\cos(\phi)$ is known as the power factor. For maximum power dissipation, the power factor, $\cos(\phi)$, must be at its maximum value, which is 1. This occurs when the phase angle $\phi = 0^\circ$. A phase angle of $0^\circ$ means that the voltage and current are in phase.

In a pure resistive circuit, the current and voltage are always in phase, meaning $\phi = 0^\circ$. Therefore, $\cos(\phi) = \cos(0^\circ) = 1$. In this case, the average power dissipated is $P_{avg} = V_{rms} 	imes I_{rms}$, which is the maximum possible power dissipation for given values of $V_{rms}$ and $I_{rms}$. This power is converted into heat.

The incorrect option is (2): In a pure capacitive circuit, the current leads the voltage by a phase angle of $90^\circ$ ($\phi = -90^\circ$ or $90^\circ$). This means $\cos(\phi) = \cos(90^\circ) = 0$. Therefore, no power is dissipated in a pure capacitive circuit over a complete cycle. The capacitor stores energy during one half-cycle and releases it back to the source in the next, resulting in zero average power dissipation.

The incorrect option is (3): In a pure inductive circuit, the voltage leads the current by a phase angle of $90^\circ$ ($\phi = 90^\circ$). This also means $\cos(\phi) = \cos(90^\circ) = 0$. Similar to a pure capacitive circuit, no power is dissipated in a pure inductive circuit over a complete cycle. The inductor stores energy in its magnetic field during one quarter cycle and returns it during the next, leading to zero average power dissipation.

The incorrect option is (4): This option is incorrect because pure resistive circuits do experience maximum power dissipation.