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 \;ω t

. The voltage is found to lead current in phase by

\;{π}/{4}

.
If the inductor is replaced by a capacitor

C

, the voltage lags behind current in phase by

\;{π}/{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

\;{X_L}/{R}=\tan 45^{∘}=1

So,

\;\; X_L=R

For CR circuit

\;{X_C}/{R}=\tan 45^{∘}=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 \;ω {\t}

{\I}\;= {\I}_0 sin \;ω {\t}

(i) Average power dissipation

{\P}= {\VI}

{\P}= {\V}_0 sin \;ω t × {\I}_0 sin \;ω t

Over full cycle

P_{A V G}=\;{V_m}/{{√{2}}} × \;{I_m}/{{√{2}}}

(ii) Instantaneous current

{\I}= {\I}_0 sin \;ω t

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