First slide

Writing potential drop across a open line

Question

One end of copper wire of length 2L and cross sectional area A is attached to one end of another copper wire of length L and cross section area 2A. If the free end of the longer wire is at electric potential of 8 volt and free end of shorter wire is at potential of 1volt,what is the potential of junction of two wires.

Moderate

A

1.2 V
B

2.1 V
C

2.4 V
D

3.6 V

Solution

$r e s i s \tan c e o f t h e l o n g e r w i r e i s R = ρ \frac{2 L}{A} a n d t h a t o f t h e s h o r t e r w i r e i s R_{2} = ρ \frac{L}{2 A} \frac{R_{1}}{R_{2}} = \frac{4}{1} i n s e r i e s p . d i s d i r e c t l y p r o p o r t i o n a l t o r e s i s \tan c e s o t o t a l p . d (8 - 1) = 7 V w i l l b e d i s t r i b u t e d 4 : 1 r a t i o p . d a c r o s s f i r s t c o n d u c t i o r \frac{7}{5} x 4 = 5.6 V p o t e n t i a l a t t h e j u n c t i o n 8 - 5.6 = 2.4 V$

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