How can you calculate the voltage across a capacitor in an RC circuit at a specific time?

V(t) = V0 * (1 - e^(-t / RC))

Where:

V(t) is the voltage across the capacitor at time t.

V0 is the initial voltage across the capacitor at t = 0.

e is the base of the natural logarithm (approximately 2.71828).

t is the time for which you want to calculate the voltage.

RC is the time constant of the RC circuit, given by the product of the resistance (R) and the capacitance (C).

Note: This formula is applicable when the capacitor is initially uncharged (i.e., V0 = 0V at t = 0) and when the capacitor is connected in series with a resistor to a DC voltage source. It represents the charging curve of a capacitor in an RC circuit.

Here's a step-by-step guide to using the formula:

Determine the values of R and C in the RC circuit.

Calculate the time constant (RC) by multiplying the resistance (R) and the capacitance (C).

Obtain the initial voltage across the capacitor (V0) at t = 0.

Choose the specific time (t) for which you want to calculate the voltage.

Plug in the values of V0, t, and RC into the formula V(t) = V0 * (1 - e^(-t / RC)).

Perform the necessary calculations to find V(t).

Keep in mind that the voltage across the capacitor will increase with time and eventually approach the maximum value of V0 as the capacitor becomes fully charged. The time it takes to reach the maximum voltage depends on the time constant RC, with a larger RC resulting in a slower charging process.