A resistor R and an inductor L are connected ...

CBSE Class 12 Physics 2020 Outside Delhi Set 1 Paper

Question : 23 of 37

Marks: +1, -0

A resistor

R

and an inductor

L

are connected in series to a source of voltage

V=V_0 \sin \omega t

. The voltage is found to lead current in phase by

\frac{\pi}{4}

If the inductor is replaced by a capacitor

C

, the voltage lags behind current in phase by

\frac{\pi}{4}

. When

L, C

and

R

are connected in series with the same source,

Find the :

(i) average power dissipated and

(ii) instantaneous current in the circuit

Solution:

For LR circuit

\frac{X_L}{R} = \tan 45^{\circ} = 1

So,

X_L = R

For CR circuit

\frac{X_C}{R} = \tan 45^{\circ} = 1

So,

X_c = R

For LCR circuit

When L, C and

R

are connected in series, then actually three

R

are connected in series. Equivalent impedance

=3 R

. Thus Circuit is resistive.

\text{ and }

V = V_0 \sin \omega t

I = I_0 \sin \omega t

(i) Average power dissipation

P = VI

P = V_0 \sin \omega t \times I_0 \sin \omega t

Over full cycle

P_{AVG} = \frac{V_m}{\sqrt{2}} \times \frac{I_m}{\sqrt{2}}

(ii) Instantaneous current

I = I_0 \sin \omega t

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