72 3
V2 æ r2 ö q = çç ÷÷ ´ 1 V1 è r1 ø q2
R R
V2 = 4 V
Þ
8. Electric field between the plates is uniform but in all other regions it is zero.
R
R
R
9. Initially the capacitor offers zero resistance. 1W E 12V
E 4E = 3 R + R 7R 4 But potential difference across capacitor, V = IR 4E 10 = R Þ 7R Þ E = 17.5 V I=
6W
3W 1W 4A 2W
12V
i=
12 =4 A 1+2
10. q = CV = CE 11. In the steady state, capacitor behaves as open circuit. the equivalent diagram is given by 3 —R 4
R
I
12. As all the capacitors are connected in series potential difference across each capacitor is E 10 V= = = 2.5 V 4 4 VA - VN = 3V = 7.5 V VA = 7.5 V VN - VB = 2.5 V VB = - 2.5 V 13. Heat produced = Loss of energy C1C2 = ( V1 - V2 )2 2 (C1 + C2 ) =
E
2 ´ 10-6 ´ 2 ´ 10-6 2 (2 + 2) ´ 10-6
(100 - 0)
= 5 ´ 10-3 J = 5 mJ
3R
q = q0e - t / h I = I0 e - t / h P = I 2 R = I02e -2t / h R = P0e -2t / h h h¢ = Þ 2 C V + C2V2 E 15. Common potential = 1 1 = 2 C1 + C2 14.
R
R
E
16. VA - VB = 6 + 3 ´ 2 -
9 + 3 ´ 3 = 12 V 1