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# A coil of inductance 0 point 50 H and resistance 100 pmega is connected to a 240 V 50 Hz ac supply.  What is the time lag between the voltage maximum and the current maximum?

Q 7.13 (b) A coil of inductance $0.50H$and resistance $100\Omega$ is connected to a $200V$$50Hz$  ac supply. What is the time lag between the voltage maximum and the current maximum?

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Let the voltage  in the circuit be

$V = V_0coswt$ and

Current in the circuit be

$I = I_0cos(wt-\phi )$

Where $\phi$ is the phase difference between voltage and current.

V is maximum At

t = 0

$I$ is maximum At

$t=\frac{w}{\phi }$

Hence, the time lag between voltage maximum and the current maximum is

$\frac{w}{\phi }$.

For phase difference $\phi$  we have

$tan\phi =\frac{wL}{R}=\frac{2\pi *50*0.5}{100}=1.57$

$\phi =57.5^0$

$t=\frac{\phi}{w}=\frac{57.5*\pi}{180*2\pi *50}=3.2ms$

Hence time lag between the maximum voltage and the maximum current is $3.2ms$

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