Time constant
Capacitors - OCR A-Level Physics
Key Definition
Time constant
The time taken for the charge (or current or p.d.) to fall to $e^{-1}$ approximately 37% of its initial value, or to rise to 63% of its final value during charging. Equal to RC.
The time taken for the charge (or current or p.d.) to fall to $e^{-1}$ approximately 37% of its initial value, or to rise to 63% of its final value during charging. Equal to RC.
$$\tau = RC$$
- After $1\tau$, $Q \approx 0.37$ Q_0. After $2\tau$, $Q \approx 0.14$ Q_0. After $5\tau$, Q < 1% of Q_0, effectively fully discharged.
- A larger time constantThe product of resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω). and capacitanceThe chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). stored per unit potential difference across a capacitor. Measured in farads (F). in an RC circuit. The time taken for the charge (or voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference.) to fall to 1/e (about 37%) of its initial value. means slower discharge: either more resistanceThe opposition to currentThe rate of flow of charge. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω). (restricts current flow) or more capacitanceThe charge stored per unit potential difference across a capacitor. Measured in farads (F). (more charge to remove).
- The time constantThe product of resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). and capacitanceThe charge stored per unit potential difference across a capacitor. Measured in farads (F). in an RC circuit. The time taken for the charge (or voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference.) to fall to 1/e (about 37%) of its initial value. can be found from the gradient of $a \ln$Q vs t graph, $since \ln$Q = $\ln$Q_0 - $\frac{t}{RC}$, giving gradient = -$\frac{1}{RC}$.
Examiner Tips and Tricks
- To find RC from experimental data, $plot \ln$(V) against t.
- The gradient is -1/RC.
- This linearises the exponential, making it easy to determine RC from a straight-line graph.