Question 26: AC fundamentals

Question

An LCR series ac circuit is at resonance with 10 V each across $\mathrm{L}, \mathrm{C}$ and R . If the resistance is halved, the respective voltage across $R, C$ and $L$ are

Accepted Answer

HereÃ¢ÂÂs the quickest way to see it:
At the original resonance
Ã¢ÂÂ $$V_R=I\,R=10	ext{ V}$$
Ã¢ÂÂ $$V_L=I\,X_L=10	ext{ V}$$
Ã¢ÂÂ $$X_L=R$$
Ã¢ÂÂ Since $$V_L$$ and $$V_C$$ cancel in phase, the supply voltage is
$$V_s=V_R=10	ext{ V}.$$
Now halve the resistance:
$$R'=	frac R2\quad\Longrightarrow\quad I'=\frac{V_s}{R'}=\frac{10}{R/2}=2I.$$
New voltage drops
Ã¢ÂÂ Across R:
$$V_R'=I'\,R'=2I\cdot\frac R2=I\,R=10	ext{ V}$$
Ã¢ÂÂ Across L (and similarly C):
$$V_L'=I'\,X_L=2I\cdot X_L=2\,(10	ext{ V})=20	ext{ V}$$
$$V_C'=20	ext{ V}$$
Answer (Option D):
RÃ¢ÂÂ10 V, CÃ¢ÂÂ20 V, LÃ¢ÂÂ20 V.

Answer

$5 \mathrm{~V}, 10 \mathrm{~V}, 10 \mathrm{~V}$

Answer

$10 \mathrm{~V}, 5 \mathrm{~V}, 5 \mathrm{~V}$

Answer

$5 \mathrm{~V}, 5 \mathrm{~V}, 5 \mathrm{~V}$

Answer

$10 \mathrm{~V}, 20 \mathrm{~V}, 20 \mathrm{~V}$

AC fundamentals

An LCR series ac circuit is at resonance with 10 V each across \mathrm{L}, \mathrm{C} and R . If the resistance is halved, the respective voltage across R, C and L are

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