Concept of Capacitors

Question

Potential across !!7muF!! capacitor is !!6V!!.

(a) !!E= 20 V!!

(b) Charge on !!1.5muF!! is !!30muC!!

(c) !!E= 26V!!

(d) Charge on !!1.5muF!! is !!20muC!!

Solution

Same charge will flow in both !!7muF!! and !!3muF!! capacitors. Voltage across !!7muF!! is given, so we can easily find !!Q_3!!.

!!Q= CV=> Q_3 = (7mu)xx6= 42muC!!

!!7muF!! and !!3muF!! is in series therefore,

!! C_(eq)= (7xx3)/(7+3) = 2.1 muF!!

Voltage across !!C_(eq)!! is,

!!V_(eq)= Q_3/C_(eq) = 42/2.1 = 20V!!

Voltage across !!1.5muF!! will be same as !!V_(eq)!!, so

!!=> Q_2 = (1.5mu)xx 20 =30mu C!!

We know that,

!! Q_1 = Q_2 + Q_3= 30 mu + 42mu = 72mu C!!

We can apply Kirchoff votlage law in Loop1,

!!Q_1/12 + Q_2/1.5 - E = 0!!

!!=> 72/12+ 30/1.5-E =0!!

!!=> 6+20-E=0!!

!!=> E= 26 V!!

Therefore options (b) and (c) are correct.