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  4. In the given circuit the R.M.S. values of voltages across the capacitor C , inductor L and resistor R1 are 12 V , 10 V and 5 V respectively. Then the peak voltage across R2 is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-hcsbqyq7vq7l.png />

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Q. In the given circuit the R.M.S. values of voltages across the capacitor $C$ , inductor $L$ and resistor $R_{1}$ are $12 \, V$ , $10 \, V$ and $5 \, V$ respectively. Then the peak voltage across $R_{2}$ is

Question

NTA AbhyasNTA Abhyas 2020

Solution:

In parallel combination each branch should have equal potential but in AC circuit in a branch,
$V _{ eff }=\sqrt{ V _{ R }^{2}+\left( V _{ c }- V _{ L }\right)^{2}}$
$V _{ C }^{2}+ V _{ R 1}^{2}= V _{ L }^{2}+ V _{ R 2}^{2}$
$\Rightarrow 12^{2}+5^{2}=10^{2}+ V _{ R 2}^{2}$
$\Rightarrow \left( V _{ R 2}\right)_{ rms }=\sqrt{69}$
$V _{ peak }=\sqrt{2} V _{ rms }$
$\therefore \quad\left( V _{ R 2}\right)_{\text {peak }}=\sqrt{138} V$