Capacitor Discharge Calculator:
Enter the values of initial voltage, Vi(V), time, t(s), resistance, R(Ω) and capacitance, C(F) to determine the values of Voltage across the discharging capacitor, Vc(V).
Capacitor Discharge Formula:
A capacitor is an electronic component that stores energy in an electric field between its plates when charged. During discharge, the stored energy is released, and the voltage across the capacitor decreases exponentially over time. The discharge occurs when the capacitor is connected to a circuit, allowing current to flow through a resistor.
The rate of discharge is determined by the time constant, which is the product of the resistance (R(Ω)) and capacitance (C(F)) in the circuit. A larger time constant results in a slower discharge rate, while a smaller time constant causes the capacitor to discharge more quickly.
The voltage across the capacitor at any time (Vc(V)) can be calculated using the exponential formula Vc(V) = Vi(V) * e-t(s) / R(Ω) * C(F), where Vi(V) is the initial voltage, ttt is the time elapsed, and e is Euler’s number (≈2.718). Initially, the discharge rate is high, but it gradually slows as the voltage approaches zero.
The exponential decay ensures that the capacitor never discharges completely, although the voltage becomes negligibly small over time. Capacitor discharge is widely used in circuits for timing, energy storage, and filtering applications. It demonstrates the interplay of resistance, capacitance, and time in controlling energy flow.
Voltage across the discharging capacitor, Vc(V) in volts at any given time, t(s) in seconds is equal to the initial voltage, Vi(V) in volts multiplied by the exponential of negative time, t(s) in seconds divided by the product of resistance, R(Ω) in Ohms and capacitance, C(F) in Farads.
Voltage across the discharging capacitor, Vc(V) = Vi(V) * e-t(s) / R(Ω) * C(F)
Vc(V) = voltage across the discharging capacitor in volts, V.
Vi(V) = initial voltage in volts, V.
t(s) = time in seconds, s.
R(Ω) = resistance in Ohms, Ω.
C(F) = capacitance in Farads, F.
Capacitor Discharge Calculation:
1.A capacitor with an initial voltage of 10V is discharging through a resistor of 2kΩ and has a capacitance of 500μF. Find the voltage after 1s.
Given: Vi(V) = 10V, t(s) = 1s, R(Ω) = 2000 Ω, C(F) = 0.0005F.
Voltage across the discharging capacitor, Vc(V) = Vi(V) * e-t(s) / R(Ω) * C(F)
Vc(V) = 10 * e– 1 / 2000 * 0.0005
Vc(V) = 10 * e-1
Vc(V) = 10 * 0.3679
Vc(V) = 3.679V.
2.A capacitor with 12V, R=1kΩ, and C=100μF discharges to a voltage of 3V. Find the time required for this discharge.
Given: Vi(V) = 10V, Vc(V) = 3.679V, R(Ω) = 2000 Ω, C(F) = 0.0005F.
Voltage across the discharging capacitor, Vc(V) = Vi(V) * e-t(s) / R(Ω) * C(F)
t(s) = – R(Ω) * C(F) * ln(Vc(V) / Vi(V))
t(s) = – 1000 * 0.0001 * ln(3 / 12)
t(s) = – 0.1 * ln(0.25)
t(s) = – 0.1 * (- 1.386)
t(s) = 0.1386s.