Question
When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit increases. Explain why.
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Answer
Impedance of series LR circuit
$\text{Z}_1=\sqrt{\text{R}^2+\text{X}^2_{\text{L}}}$
When capacitor is also connected in circuit,
Then impedance
$\text{Z}_{\text{L}}=\sqrt{\text{R}^2+(\text{X}_{\text{L}}-\text{X}_{\text{C}})^2}$
Clearly impedance of circuit decreases $(Z_2 < Z_1)$, so the value of current $\text{I}=\frac{\text{v}}{\text{z}}\propto\frac{1}{\text{z}}$ in the circuit increases.
$\text{Z}_1=\sqrt{\text{R}^2+\text{X}^2_{\text{L}}}$
When capacitor is also connected in circuit,
Then impedance
$\text{Z}_{\text{L}}=\sqrt{\text{R}^2+(\text{X}_{\text{L}}-\text{X}_{\text{C}})^2}$
Clearly impedance of circuit decreases $(Z_2 < Z_1)$, so the value of current $\text{I}=\frac{\text{v}}{\text{z}}\propto\frac{1}{\text{z}}$ in the circuit increases.
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