Question

A series combination of two capacities of value 0.1 microfarad and 1 microfarad is connected with a source of voltage 500 volts. The potential difference in volts across the capacitor of value 0.1 microfarad will be :
(1) 50
(2) 500
(3) 45.5
(4) 454.5

Answer 1

let capacitor 0.1 mircofarad be C1 and 1 microfarad be C2.
when capacitors are in series,
1/C12 = 1/C1 + 1/C2
therefore, C12= C1*C2/(C1 + C2)
C12 = 0.1*1/(1+0.1)
= 0.091 microfarad
therefore charge, Q = C12*v
= 0.091*500
= 45.5 mC
charge across both capacitor will be same;
that is charge across C1 is Q =45.5 mC
and C2 is Q =45.5
therefore potential difference across 0.1 microfarad is;
V1 = Q/C1
= 45.5/0.1
= 455
which nearly close to 454.5, option 4.