Question

Can the peak voltage across the inductor be greater than the peak voltage of the source in an LCR circuit?

Answer 1

Let a LCR circuit is connected across an AC supply with the emf E = E₀ sin ωt.
Let the inductance in the circuit be L
Let the net impedence of the circuit be Z = `sqrt(R^2 + (X_L -X_c)^2`
Where,
R =  resistance in the circuit
X_L = reactance due to inductor
X_C = reactance due to capacitor
The magnitude of the voltage across the inductor is given by
`V = L(di)/(dt)`
The current in the circuit can be written as `I = I_0 sin (wt + Ø)`
Where, ϕ is the phase difference between the current and the supply voltage
Thus, the voltage across the inductor can be written as
`V = LI_0`

⇒ `V = (E_0)/(Z)xxL,`
Therefore, the peak voltage across the inductor is given by `V = (E_0)/RxxL`
if `L/R xx L,`
if L/R > 1
V > E₀
Therefore if magnitude of  `L/R >1` at resonance the value of the voltage across the inductor will bw greater than the peak value of the supply voltage.