17.9 Impendance

17.9 Impendance

In AC circuits, the opposition to current flow is called impedance denoted by $Z$, which includes both resistance $R$ and reactance $X$. The resistance $R$ is the opposition to current flow due to resistors. Reactance is the opposition to current flow due to capacitors (capacitive reactance $X_{C}$) and inductors (inductive reactance $X_{L}$). A pure resistive circuit has only resistance $R$ and no reactance.

The combined effect of resistance and reactances in such circuits is known as impedance. It is the ratio of the rms value of the voltage to the rms value of the current. Thus,

This SI unit of impedance is ohm.

Example 17.5

An AC circuit operates by a peak voltage of $200\,\mathrm{V}$ and $10\,\mathrm{A}$ as peak input current. Find the impedance of the circuit.

Solution

Peak voltage $V_{o} = 200\,\mathrm{V}$, Peak current $I_{o} = 10\,\mathrm{A}$ We know that; $V_{\mathrm{rms}} = V_{o} \times 0.707 = 200\,\mathrm{V} \times 0.707 = 141.4\,\mathrm{V}$ and $I_{\mathrm{rms}} = I_{o} \times 0.707 = 10\,\mathrm{A} \times 0.707 = 7.07\,\mathrm{A}$ As impedance $Z = \dfrac{V_{\mathrm{rms}}}{I_{\mathrm{rms}}}$ , therefore, $Z = \dfrac{141.4\,\mathrm{V}}{7.07\,\mathrm{A}} = 20\,\Omega$