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Question: In the following circuit diagram fig. the lengths of the wires *AB* and *BC* are same but the radius...

In the following circuit diagram fig. the lengths of the wires AB and BC are same but the radius of AB is three times that of BC. The ratio of potential gradients at AB and BC will be

A

1 : 9

B

9 : 1

C

3 : 1

D

1 : 3

Answer

1 : 9

Explanation

Solution

x∝Rp∝1r2x \propto R _ { p } \propto \frac { 1 } { r ^ { 2 } } ⇒ x1x2=r22r12=(r3r)2=19\frac { x _ { 1 } } { x _ { 2 } } = \frac { r _ { 2 } ^ { 2 } } { r _ { 1 } ^ { 2 } } = \left( \frac { r } { 3 r } \right) ^ { 2 } = \frac { 1 } { 9 }