given:
Inductance \(L=10 H\),
Resistance \(R=500 \Omega\), voltage across the \(\operatorname{cct} V_{ rms }=20 V\),
\(f=50 Hz\)
Required : \(V _{\text {peak }}\) or \(V _{0}\) across the inductor \(=\) ?
correlating equations
\(V_{r, m, s}=\frac{V_{o}}{\sqrt{2}}\).
Note:
It will be wrong to say
\(V_{i j}=20 \sqrt{2}=28,284 V\)
This approach is wrong because the question requested we calculate the peak voltage across the inductor and not the peak voltage across the circuit. The correct approach will be to calculate first the r.m.s voltage across the inductor and use equation (I) above to obtain the required peak voltage.
thus:y Pythagoras' theorem,
\(V=\sqrt{V_{R}^{2}+V_{L}^{2}}\)
but \(V=I Z, V_{R}=I R, V_{L}=I X_{L}\)
Where \(I=\) current in the circuit
\(Z=\) total resistance or impedance of the circuit
\(X_{L}=\) resistance of the inductor or simply inductive reac-
tance.
\(I Z=\sqrt{I^{2} R^{2}+I^{2} X_{L}^{2}}\) \(I Z=\sqrt{I^{2}\left(R^{2}+X_{L}^{2}\right)}\)
or
\(I Z=\sqrt{I^{2}} x \sqrt{R^{2}+X_{L}^{2}}\) \(I Z=I \sqrt{R^{2}+X_{L}^{2}}\)
we divide through by I to obtain
\(Z=\sqrt{R^{2}+X_{L}^{2}}\)