Calculate the following:
- Impedance of the given ac circuit.
- Wattless current of the given ac circuit.
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- Potential difference across capacitance, $V_C = X_C\ I$
$\text{X}_{\text{C}}=\frac{\text{V}_{\text{C}}}{\text{I}}=\frac{40}{2}=20\Omega$
Resistance, $\text{R}=\frac{\text{V}_{\text{R}}}{\text{I}}=\frac{30}{2}=15\Omega$
Impedance, $\text{Z}=\sqrt{\text{R}^2+\text{X}^2_{\text{C}}}=\sqrt{(15)^2+(20)^2}$
$=\sqrt{225+400}=\sqrt{625}\Omega=25\Omega$
The phase lead $(\varphi)$ of current over applied voltage is
$\varphi=\frac{\text{X}_{\text{C}}}{\text{R}}$
Wattless Current, $\text{I}_{\text{wattless}}=\text{I}\sin\varphi=\text{I}\Big(\frac{\text{X}_{\text{C}}}{\text{Z}}\Big)$
$=2\times\frac{20}{25}\text{A}=1.6\text{A}$
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