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Physics Question on electrostatic potential and capacitance

the charge on capacitors C1C_{1} and C4C_{4} are

A

4×10−3 C,12×10−3 C4 \times 10^{-3}\, C, 12 \times 10^{-3} \, C

B

6×10−3 C,12×10−3 C6 \times 10^{-3}\, C, 12 \times 10^{-3} \, C

C

2×10−3 C,4×10−3 C2 \times 10^{-3}\, C, 4 \times 10^{-3} \, C

D

3×10−3 C,2×10−3 C3 \times 10^{-3}\, C, 2 \times 10^{-3} \, C

Answer

4×10−3 C,12×10−3 C4 \times 10^{-3}\, C, 12 \times 10^{-3} \, C

Explanation

Solution

Charge on each capacitor, C1,C2,C3C_{1}, C_{2}, C_{3} is same =q= q Let charge on C4C_{4} be qq' ∴qC1+qC2+qC3=600\therefore \frac{q}{C_{1}}+\frac{q}{C_{2}}+\frac{q}{C_{3}}=600 or q[1C1+1C2+1C3]=600q\left[\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\right]=600 or qCs=600\frac{q}{C_{s}}=600 ∴q=600Cs=600×203μC\therefore q=600 C_{s}=600\times\frac{20}{3} \mu C 4000×10−6C=4×10−3C4000\times10^{-6}C=4\times10^{-3}C Also q′C4=600\frac{q'}{C_{4}}=600 or q′=C4×600μCq'=C_{4}\times600 \mu C =200×600 μC=200\times600\, \mu C =12×10−3C=12\times10^{-3} C