Question

In an LRC series circuit, can the instantaneous voltage across the capacitor exceed the source voltage at that same instant? Can this be true for the instantaneous voltage across the inductor and across the resistor? Explain.

Short answer

The instantaneous voltage across the capacitor cannot exceed the source voltage at that same instant. This is also true for instantaneous voltage across inductor and resistor.

Step-by-step solution

Define instantaneous voltage and Kirchhoff’s voltage law

When inductor, capacitor and resistor are connected in series with an ac power supply, the circuit is called LCR series ac circuit.

AC power supply provides variable voltage. This voltage varies with time only. So, the voltage at any given instant of time is called instantaneous voltage.

Kirchhoff’s voltage law states that the voltage around a loop equals the sum of every voltage drop in the same loop for any closed network and equals zero.

Apply Kirchhoff’s voltage law

Voltage at any instant provide by ac power supply must be equal to instantaneous voltage across each electrical component (resistor, inductor and capacitor) in circuit as per Kirchhoff’s voltage law.

$V_{ac}=V_R+V_L+V_c$Whererole="math" localid="1663856786161" $V_{ac}$ is voltage provided by AC supply at an instant,$V_R$ is the voltage across resistor at same instant,role="math" localid="1663856763293" $V_L$ is the voltage across inductor at same instant$V_c$ and is the voltage across capacitor at same instant.

From above expression it is clear that$V_{ac}>V_c$ the instantaneous voltage across the capacitor cannot exceed the source voltage at that same instant. Similarly,role="math" localid="1663856841295" $V_{ac}>V_R$ and $V_{ac}>V_c$.

Therefore, the instantaneous voltage across the capacitor, inductor and resistor cannot exceed the source voltage at that same instant.