Concepts Of Physics MCQ Edition [Volume 2]PhysicsCapacitors
Determine the equivalent capacitances between the specified points for the combinations illustrated in the figure.
Options
- A(a) 11 4 F , (b) 11 6 F , (c) 8 F , (d) 8 F
- B(a) 11 6 F , (b) 11 4 F , (c) 12 F , (d) 16 F
- C(a) 11 6 F , (b) 11 4 F , (c) 8 F , (d) 8 F
- D(a) 2 F , (b) 4 F , (c) 8 F , (d) 8 F
Correct answer
C. (a) 11 6 F , (b) 11 4 F , (c) 8 F , (d) 8 F
Step-by-step solution
For circuit (a): Let the input node be at potential V and the output node be at 0 . Let the potentials at the top and bottom junctions be x and y respectively. Applying Kirchhoff's Current Law (KCL) at the top junction: (x - V) 1 + (x - 0) 3 + (x - y) 4 = 0 8x - 4y = V Applying KCL at the bottom junction: (y - V) 3 + (y - 0) 1 + (y - x) 4 = 0 -4x + 8y = 3V Solving these two equations, we get x = 5V 12 and y = 7V 12 . The total charge Q supplied by the source is the sum of charges on the input capacitors: Q = (V - x