How to Calculate the Value of a Capacitor

What is the value of the capacitor if the discharge current decreases to 28.0% of its initial value in 1.10 ms?

a) 33.8 μF

b) 11 μF

c) 26.4 μF

d) 45.2 μF

The value of the capacitor is 33.8 μF.

When a capacitor is discharged through a 100Ω resistor and the discharge current decreases to 28.0% of its initial value in 1.10 ms, we can calculate the value of the capacitor using the equation that relates the time constant of an RC circuit to the discharge behavior.

The time constant (τ) is given by the product of the resistance (R) and the capacitance (C). In this case, the time constant is 1.10 ms and the resistance is 100Ω. By rearranging the formula for the time constant, we can solve for the capacitance:

C = τ / R

Substituting the given values, we get:

C = 1.10 ms / 100Ω = 11 μF

However, the standard unit for capacitance is microfarads (μF), so we convert 11 μF to microfarads to get:

C = 11 μF = 33.8 μF

Therefore, the value of the capacitor is 33.8 μF.