In many electronic circuits, a voltage source does not immediately appear across the load because the capacitor must first charge. The delay is governed by the circuit’s time constant, τ = RC. Despite this lag, an instantaneous voltage can be calculated at any moment using the standard RC charging equation.

Step 1 – Select the Resistor (R)

For this example, choose R = 40 Ω.

Step 2 – Choose the Capacitor (C)

For this example, choose C = 12 µF.

Step 3 – Compute the Time Constant (τ)

τ = R × C = 40 Ω × 12 µF = 480 µs.

Step 4 – Apply the RC Charging Formula

The voltage across the capacitor at time t is:

V(t) = V₀ (1 – e^–t/τ)

where V₀ is the supply voltage and t is the elapsed time since the supply was applied.

Example Calculation

Assume a supply voltage V₀ = 120 V and we want the voltage after t = 1 µs.

t/τ = 1 µs ÷ 480 µs = 0.002.

e^–t/τ = e^–0.002 ≈ 0.998.

V(1 µs) = 120 V (1 – 0.998) = 120 V × 0.002 ≈ 0.24 V.

Thus, at one microsecond after the supply is applied, the instantaneous voltage across the capacitor is approximately 0.24 V, despite the 480 µs time constant required for the voltage to reach its steady‑state value.