First slide

AC Circuits

Question

Same current is flowing in two alternating circuits. The first circuit contains only inductance and the other contains only a capacitor. If the frequency of the e.m.f. of ac is increased, the effect on the value of the current will be

Moderate

A

Increases in the first circuit and decreases in the other
B

Increases in both the circuits
C

Decreases in both the circuits
D

Decreases in the first circuit and increases in the other

Solution

For the first circuit $i = \frac{V}{Z} = \frac{V}{\sqrt{R^{2} + ω^{2} L^{2}}}$
$∴$ Increase in $ω$ will cause a decrease in i.
For the second circuit $i = \frac{V}{\sqrt{R^{2} + \frac{1}{ω^{2} C^{2}}}}$
$∴$ Increase in $ω$ will cause an increase in i.

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