Question

A coil of reactance 100 ohm and resistance 100 ohm is connected to a 240 V, 50 Hz a.c. supply.(a) What is the maximum current in the coil ?(b) What is the time lag between the voltage maximum and the current maximum ?​

Answer 1

(a) Maximum current will be equal to 2.399 A

(b) Time lag between voltage and current will be 0.0025 sec

Explanation:

We have given coil of reluctance 100 ohm

So inductive reactance $X_l=100ohm$

Resistance R = 100 ohm

So impedance of the circuit $Z=\sqrt{R^2+X_l^2}=\sqrt{100^2+100^2}=100\sqrt{2}=100\times 1.414=141.4ohm$

Now current in the circuit will be the ratio of voltage and impedance

So current $i=\frac{V}{Z}=\frac{240}{141.4}=1.697A$

(a) Maximum current in the circuit will be $I_{max}=\sqrt{2}i=1.414\times 1.697=2.399A$

(b) Now angle between voltage and current $cos\Theta =\frac{R}{Z}=\frac{100}{141.4}=0.707$

$\Theta =cos^{-1}0.707=45^{\circ}$ = $\frac{\pi }{4}$

Frequency is given 50 Hz

So angular frequency $\omega =2\pi f=2\times 3.14\times 50=314rad/sec$

We know that $\Theta =\omega t$

$\frac{\pi }{4} =314\times t$

t = 0.0025 sec  

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