Edexcel A Level (IAL) Physics-4.22 Charge & Discharge Curves- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -4.22 Charge & Discharge Curves- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -4.22 Charge & Discharge Curves- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
RC Circuits: Charge and Discharge Curves & the Time Constant \( RC \)
An RC circuit consists of a resistor and a capacitor connected in series. When connected to a d.c. supply, the capacitor charges; when disconnected and allowed to empty through the resistor, it discharges.
Charging a Capacitor in an RC Circuit
When a capacitor is connected to a battery through a resistor:
- Charge on the capacitor increases with time.
- Potential difference across the capacitor increases.
- Current in the circuit decreases with time.
Key equations during charging:
\( Q = CV\left(1 – e^{-t/RC}\right) \)
\( V_C = V\left(1 – e^{-t/RC}\right) \)
\( I = \dfrac{V}{R} e^{-t/RC} \)
Interpreting Charging Curves
- The charge–time and voltage–time graphs rise exponentially.
- The current–time graph falls exponentially.
- The capacitor never becomes fully charged instantly.
- As \( t \to \infty \), current approaches zero.
Discharging a Capacitor in an RC Circuit
When a charged capacitor is allowed to discharge through a resistor:
- Charge on the capacitor decreases with time.
- Potential difference across the capacitor decreases.
- Current decreases with time.
Key equations during discharging:
\( Q = Q_0 e^{-t/RC} \)
\( V = V_0 e^{-t/RC} \)
\( I = I_0 e^{-t/RC} \)
Interpreting Discharge Curves
- Charge, voltage, and current decrease exponentially.
- None of these quantities reach zero instantly.
- The curve is steep at first and then gradually flattens.
The Time Constant \( RC \)
The time constant of an RC circuit is defined as:
\( \tau = RC \)
- \( R \) = resistance (Ω)
- \( C \) = capacitance (F)
- \( \tau \) = time constant (s)
Physical Significance of the Time Constant
Charging:
- After time \( RC \), the charge and voltage reach about 63% of their final values.
Discharging:
- After time \( RC \), the charge and voltage fall to about 37% of their initial values.
Rule of thumb:
- After \( 5RC \), charging or discharging is effectively complete.
Effect of Changing \( R \) or \( C \)
- Increasing \( R \) increases the time constant → slower charging/discharging.
- Increasing \( C \) increases the time constant → slower charging/discharging.
- Decreasing either makes the process faster.
Example (Easy)
A capacitor of \( 1000\ \mathrm{\mu F} \) is connected in series with a \( 2.0\ \mathrm{k\Omega} \) resistor. Calculate the time constant.
▶️ Answer / Explanation
\( \tau = RC = 2000 \times 1000\times10^{-6} = 2.0\ \mathrm{s} \)
Example (Medium)
State the fraction of maximum charge on a capacitor after one time constant during charging.
▶️ Answer / Explanation
After one time constant, charge ≈ \( 0.63Q_{\text{max}} \)
Example (Hard)
A charged capacitor discharges through a resistor with time constant \( 4.0\ \mathrm{s} \). Find the fraction of its initial voltage remaining after \( 4.0\ \mathrm{s} \).
▶️ Answer / Explanation
Use the discharge equation:
\( \dfrac{V}{V_0} = e^{-t/RC} = e^{-1} \approx 0.37 \)
Voltage remaining ≈ 37%