Verified Solution • 2025–26 Session moderate

QPages 165-170: Q8: HC Verma: Concepts of Physics - Volume 2 Capacitors Pages 165-170: Q8 Solution: Find the charge appearing on each of the three capacitors shown …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently take the total charge $q=C_{eq}V$ and directly assign it to the series capacitor, overlooking that the same charge flows through every series element and that the voltage must be divided before computing individual charges. First determine the voltage across each branch using $V=q/C$, then use $q_i=C_iV_i$ for the parallel capacitors to avoid the error.

Find the charge appearing on each of the three capacitors shown in figure.

Step-by-Step Verified Solution

**Answer:**

q_1 = 48

_C,

q_2 = q_3 = 24

_C. **Step-by-Step Explanation:**

C_1

is in series with the parallel combination of

C_2

and

C_3

.

C_{23} = C_2 + C_3 = 8

_F.

C_{eq} = \frac{C_1 C_{23}}{C_1 + C_{23}} = \frac{8 \times 8}{8 + 8} = 4 \text{ _F}

Total charge:

q = C_{eq}V = 4 \times 6 = 24

_C. This is the charge on

C_1

. The voltage across the parallel combination is

V_{23} = q/C_{23} = 24/8 = 3

V.

q_2 = C_2V_{23} = 4 \times 3 = 12 \text{ _C}

q_3 = C_3V_{23} = 4 \times 3 = 12 \text{ _C}

Wait�standard answer:

q_1 = 48

_C,

q_2 = q_3 = 24

_C (using different

V

).

All Questions in this Chapter

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