Question
When a capacitor is joined with a series LR circuit in series, then current flowing through the circuit increases. Explain, why?
✓
Answer
Impedance of L-R circuit
$ Z_1=\sqrt{R^2+(\rho L)^2} \quad
\therefore \text { Current } I_1=\frac{E}{Z_1} $
On joining capacitor, impedance of LCR circuit
$Z _2=\sqrt{ R ^2+\left(\omega L -\frac{1}{\omega C }\right)^2} \therefore$ Current $I _2=\frac{ E }{ Z _2}$
$\therefore \quad \frac{ I _2}{ I _1}=\frac{ Z _1}{ Z _2}$
Since, $Z_1>Z_2$ Hence $\quad I _2> I _1$
$ Z_1=\sqrt{R^2+(\rho L)^2} \quad
\therefore \text { Current } I_1=\frac{E}{Z_1} $
On joining capacitor, impedance of LCR circuit
$Z _2=\sqrt{ R ^2+\left(\omega L -\frac{1}{\omega C }\right)^2} \therefore$ Current $I _2=\frac{ E }{ Z _2}$
$\therefore \quad \frac{ I _2}{ I _1}=\frac{ Z _1}{ Z _2}$
Since, $Z_1>Z_2$ Hence $\quad I _2> I _1$
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