Concept:When two charged capacitors with the same polarity are connected in parallel, the total charge is conserved, and they share a common potential.
Explanation:The total charge before connecting the capacitors is:
Qtotal=C1V1+C2V2After connecting them in parallel, both capacitors acquire the same common potential
V.
The total charge in this condition is:
Qtotal=(C1+C2)VBy conservation of charge:
(C1+C2)V=C1V1+C2V2Therefore, the common potential is:
V=C1+C2C1V1+C2V2Substitute
C1=100×10−6 F,
V1=20 V,
C2=50×10−6 F, and
V2=40 V:
V=(100×10−6)+(50×10−6)(100×10−6)(20)+(50×10−6)(40)V=150×10−62×10−3+2×10−3V=1.5×10−44×10−3=380 V
Answer:The common potential of the parallel combination is
380 V.
Hence, the correct option is D.