# A Resistance 'R' Draws Power 'P' When Connected To An Ac Source. If An Inductance Is Now Placed In Series With The Resistance, Such That The Impedance Of The Circuit Becomes 'Z', The Power Drawn Will Be

A Resistance ‘R’ Draws Power ‘P’ When a resistor is connected to an AC source, the power drawn will be

P = $$V_{rms} * I_{rms}$$

= $$V_{rms} * \frac{V_{rms}}{R}$$

= $$V^{2}_{rms}$$

= PR

When an inductor is connected in series with the resistor, then the power drawn will be

$${P}’ = V_{rms} * I_{rms} cos\Phi$$

Where$$\Phi$$ is the phase difference

Thereofre, $${P}’ = V_{rms} * I_{rms} cos\Phi$$ $${P}’ = \frac{V^{2}_{rms}}{R} * \frac{R^{2}}{Z^{2}}$$

= $$P * R * \frac{R^{2}}{Z^{2}}$$ $${P}’ = \frac{P * R^{2}}{Z^{2}}$$ $${P}’ = P\left(\frac{R}{Z}\right)^{2}$$

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