Q15 (2024)
Five capacitors of capacitances $C_{1}=C_{2}=C_{3}=C_{4}=10\mu F$ and $C_{5}=2.5\mu F$ are connected as shown, along with a battery of 50 V.
{{IMG1}}
The equivalent capacitance and the charges on each capacitor respectively are:
- 5 $\mu$ F, 125 $\mu$ C on all capacitors
- 5 $\mu$ F, 250 $\mu$ C on all capacitors
- 4 $\mu$ F, 250 $\mu$ C on $C_{1}$ to $C_{4}$ and 125 $\mu$ C on $C_{5}$
- 5 $\mu \mathrm{F}, 125 \mu \mathrm{C}$ on $\mathrm{C}_{1}$ to $\mathrm{C}_{4}$ and $25 \mu \mathrm{C}$ on $\mathrm{C}_{5}$
### Related Formula
$$C_{\text{series}} = \frac{C}{n}$$
$q = C V$
### Core Logic
$C_1, C_2, C_3, C_4$ in series give $C_{1-4} = \frac{10}{4} = 2.5 \mu\mathrm{F}$.
{{SOL_IMG1}}
$$C_{\text{eq}} = 2.5 + 2.5 = 5 \mu\mathrm{F}$$
$$q_1 = q_2 = q_3 = q_4 = 2.5 \times 50 = 125 \mu\mathrm{C}$$
$$q_5 = 2.5 \times 50 = 125 \mu\mathrm{C}$$
### Pattern Recognition
Series combination of equal capacitors connected in parallel with a fifth capacitor.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Electrostatic Potential and Capacitance
