Difference between revisions of "Dicharging a Capacitor"

Revision as of 17:55, 22 May 2024

Key Stage 5

Meaning

Capacitor discharge is the process of releasing the stored energy in a capacitor through a circuit.

About Capacitor Discharge

The voltage and current also decrease exponentially during discharge.
The time constant determines how quickly a capacitor discharges.
A large time constant means a slow discharge, while a small time constant means a rapid discharge.
Capacitor discharge curves are used to analyze the behaviour of RC circuits.
Safety precautions are necessary when discharging large capacitors to avoid electric shock.

Formula

The discharge through a resistor follows an exponential decay described by the formulae:

\(𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}\)

\(V=V_0𝑒^{−𝑡/𝑅𝐶}\)

\(I=I_0𝑒^{−𝑡/𝑅𝐶}\)

Where:

𝑅 is the resistance in the circuit,

𝐶 is the capacitance of the capacitor,

𝑡 is time,

𝑄 is the charge stored at time t,

V is the potential difference across the capacitor at time t,

I is the current being discharged by the capacitor at time t,

𝑄₀ is the initial charge stored,

V₀ is the initial potential difference across the capacitor,

I₀ is the initial current through the circuit

A capacitor's rate of discharge in a circuit is characterised by the time constant 𝜏 which is given by the formula:

𝜏 = 𝑅𝐶

Examples

In a defibrillator, the capacitor discharges its energy quickly to deliver a shock to a patient's heart. In RC timing circuits, capacitors discharge to control the timing intervals.

@@ Line 12: / Line 12: @@
 ===Formula===
-The '''discharge''' through a [[resistor]] follows an [[Exponential Decay|exponential decay]] described by the formula:
+The '''discharge''' through a [[resistor]] follows an [[Exponential Decay|exponential decay]] described by the formulae:
 *<math>𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}</math>
-*<math>𝑄=𝑄_0𝑒^\frac{−𝑡}{𝑅𝐶}</math>
+*<math>V=V_0𝑒^{−𝑡/𝑅𝐶}</math>
+*<math>I=I_0𝑒^{−𝑡/𝑅𝐶}</math>
 Where:
-𝑄 is the [[Electrical Charge|charge]] stored,
+𝑅 is the [[Electrical Resistance|resistance]] in the [[Electrical Circuit|circuit]],
+𝐶 is the [[capacitance]] of the [[capacitor]],
+𝑡 is [[time]],
-𝑄<sub>0</sub> is the initial [[Electrical Charge|charge]] stored,
+𝑄 is the [[Electrical Charge|charge]] stored at time t,
+V is the [[Potential Difference|potential difference]] across the [[capacitor]] at time t,
-𝑅 is the [[Electrical Resistance|resistance]] in the [[Electrical Circuit|circuit]],
+I is the [[Electrical Current|current]] being discharged by the [[capacitor]] at time t,
-𝐶 is the [[capacitance]] of the [[capacitor]]
+𝑄<sub>0</sub> is the initial [[Electrical Charge|charge]] stored,
-and
+V<sub>0</sub> is the initial [[Potential Difference|potential difference]] across the [[capacitor]],
-𝑡 is [[time]]
+I<sub>0</sub> is the initial [[Electrical Current|current]] through the [[Electrical Circuit|circuit]]
 A [[capacitor]]'s rate of '''discharge''' in a [[Electrical Circuit|circuit]] is characterised by the [[Capacitor Time Constant|time constant]] 𝜏 which is given by the formula: