Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# Can the Peak Voltage Across the Inductor Be Greater than the Peak Voltage of the Source in an Lcr Circuit? - Physics

Short Note
Sum

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

#### Solution

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
XL = reactance due to inductor
XC = 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.

Concept: Peak and Rms Value of Alternating Current Or Voltage
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 17 Alternating Current
Short Answers | Q 4 | Page 328