Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Current in Conductors
Determine the equivalent resistances between the points a and b for the networks depicted in the given figure.
Options
- A(a) 5 8 r , (b) 4 3 r , (c) r , (d) r 4 , (e) r
- B(a) 5 8 r , (b) 3 4 r , (c) r , (d) r 4 , (e) r 2
- C(a) 5 8 r , (b) 4 3 r , (c) r 2 , (d) r 4 , (e) r
- D(a) 3 8 r , (b) 4 3 r , (c) r , (d) r 2 , (e) r
Correct answer
A. (a) 5 8 r , (b) 4 3 r , (c) r , (d) r 4 , (e) r
Step-by-step solution
For network (a), let the nodes be a (bottom-left), b (bottom-right), C (top-left), and D (top-right). The resistors between C and D, and D and b are in series. Their equivalent resistance is r + r = 2r . This combination is in parallel with the diagonal resistor between C and b . The equivalent resistance is 2r r 2r + r = 2r 3 . This is in series with the resistor between a and C. The equivalent resistance of this upper branch is r + 2r 3 = 5r 3 . Finally, this upper branch is in parallel with the resistor between