# (a) In an RLC circuit, can the amplitude of the voltage across an indu

(a) In an RLC circuit, can the amplitude of the voltage across an inductor be greater than the amplitude of the generator emf? (b) Consider an RLC circuit with emf amplitude
${\xi }_{m}=10V$
, resistance $R=10\mathrm{\Omega }$, inductance $L=1.0H$, and capacitance
$C=1.0\mu F$. Find the amplitude of the voltage across the inductor at resonance.
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Step 1
Part a)
Maximum current is:
$I=em\frac{f}{Z}$
Maximum voltage across the inductor is:

Therefore if XL be greater than Z, then the voltage across the inductor will be greater than the emf.
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Step 2
Part b)
$\omega =\sqrt{\frac{1}{L}C}=\frac{1}{\sqrt{\left(1.0\right)\cdot \left(1e-6\right)}}=1000ra\frac{d}{s}$
${X}_{L}=\omega L=1000\cdot 1.0=1000ohms$
At resonance: $Z=R=10ohms$; therefore:
${V}_{L}=emf\left(\frac{{X}_{L}}{Z}\right)=10\cdot \frac{1000}{10}=1000V=1.0kV$