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- Capacitance
NEET · Physics · Capacitance
A network consisting of three resistors, three batteries, and a...
A network consisting of three resistors, three batteries, and a capacitor is shown in figure.
| Column I | Column II | ||
| (A) | Current in branch EB | (P) | 10 \muC |
| (B) | Current in branch CB | (Q) | 0.5 A |
| (C) | Current in branch ED | (R) | 1.5 A |
| (D) | Charge on capacitor | (S) | 5 \muC |
| (T) | None of these |
Options
- A(\mathrm{A} \rightarrow \mathrm{R}, \mathrm{B} \rightarrow \mathrm{Q}, \mathrm{C} \rightarrow \mathrm{Q}, \mathrm{D} \rightarrow \mathrm{P})
- B(\mathrm{A} \rightarrow \mathrm{R}, \mathrm{B} \rightarrow \mathrm{Q}, \mathrm{C} \rightarrow \mathrm{R}, \mathrm{D} \rightarrow \mathrm{S})
- C(\mathrm{A} \rightarrow \mathrm{Q}, \mathrm{B} \rightarrow \mathrm{R}, \mathrm{C} \rightarrow \mathrm{R}, \mathrm{D} \rightarrow \mathrm{P})
- D(\mathrm{A} \rightarrow \mathrm{R}, \mathrm{B} \rightarrow \mathrm{Q}, \mathrm{C} \rightarrow \mathrm{Q}, \mathrm{D} \rightarrow \mathrm{S})
Correct answer
A. (\mathrm{A} \rightarrow \mathrm{R}, \mathrm{B} \rightarrow \mathrm{Q}, \mathrm{C} \rightarrow \mathrm{Q}, \mathrm{D} \rightarrow \mathrm{P})
Step-by-step solution
When a steady state is reached, no current passes through the capacitor or the branch CE.
Considering the loop ABEFA,
(5 \times\left(\mathrm{i}_1+\mathrm{i}_2\right)=10 \text{ or } \mathrm{i}_1+\mathrm{i}_2=2 \mathrm{ A} \ldots \text{ (i) })
Considering the loop BCDEB
(4 \mathrm{i}_2=12-10=2 \Rightarrow \mathrm{i}_2=0.5 \mathrm{ A})
So (\mathrm{i}_1=2-0.5=1.5 \mathrm{ A})
To find the charge on capacitors, we must know potential difference across the plates.
Consider the loop CEDC :
(-12+4 \mathrm{i}_2+3 \times 0-\mathrm{V}_{\mathrm{C}}+8=0 \Rightarrow \mathrm{ V}_{\mathrm{C}}=-2 \mathrm{ V})
So charge on capacitor (=10 \mu \mathrm{C})