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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Current in Conductors

A 6 -volt battery with negligible internal resistance is connected across a uniform wire AB of length 100 cm . As shown in the figure, the positive terminal of another battery having an emf of 4 V and an internal resistance of 1 is joined to point A . Assume the potential at B is zero. Determine the following: (i) The potentials at points A and C . (ii) The distance from A to the point D on the wire AB where the pote

Options

  1. A(i) 6 V , 2 V ; (ii) 33.3 cm ; (iii) 1 A ; (iv) 6 V , -1.5 V , 25 cm
  2. B(i) 4 V , 2 V ; (ii) 50 cm ; (iii) zero; (iv) 4 V , -3.5 V , no such point exists
  3. C(i) 6 V , 2 V ; (ii) 66.7 cm ; (iii) zero; (iv) 6 V , -1.5 V , no such point exists
  4. D(i) 6 V , 4 V ; (ii) 33.3 cm ; (iii) 2 A ; (iv) 6 V , 1.5 V , 75 cm

Correct answer

C. (i) 6 V , 2 V ; (ii) 66.7 cm ; (iii) zero; (iv) 6 V , -1.5 V , no such point exists

Step-by-step solution

Given V_B = 0 V . The 6 V battery is connected across the wire AB with its positive terminal at A . V_A - V_B = 6 V V_A = 6 V In the lower branch, the 4 V battery has its positive terminal at A . Since the circuit is open at C , no current flows through the 1 resistor, meaning there is no voltage drop across it. V_A - V_C = 4 V V_C = 6 - 4 = 2 V Let D be at a distance x from A . The potential gradient along the wire AB of length 100 cm is: = V_A - V_B L = 6 100 = 0.06 V/cm The potential at D is given by: V_D = V_A

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