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  4. In a series R L C circuit, potential differences across R, L and C are 30 V , 60 V and 100 V respectively as shown in figure. The e.m.f. of source (in volts) is

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Q. In a series $R L C$ circuit, potential differences across $R, L$ and $C$ are $30\, V , 60 \,V$ and $100 \,V$ respectively as shown in figure. The e.m.f. of source (in volts) is

Alternating Current

Solution:

emf $=V_{\text{rms }}=\sqrt{V_{R}^{2}+\left(V_{L}-V_{c}\right)^{2}}$
$=\sqrt{(30)^{2}+(100-60)^{2}}$
$=\sqrt{(30)^{2}+(40)^{2}}=50 \,V$