NEET-XII-Physics
32: Electric Current in Conductors
- #37In the circuit shown in the figure (32-E13), ε1 = 3 V, ε2 = 2 V, εa = 1 V and r1 = r2 = r3 = 1Ω. Find the potential difference between the points A and B and the current through each branch.
figure 32-E13
Ans :
Applying KVL in loop 1, we get:
`` {i}_{1}+\left({i}_{1}-{i}_{2}\right)-1+2=0``
`` 2{i}_{1}-{i}_{2}=-1...\left(1\right)``
`` ``
Similarly, for loop 2:
`` {i}_{2}-\left({i}_{1}-{i}_{2}\right)-2+3=0``
`` 2{i}_{2}-{i}_{1}=-1...\left(2\right)``
Solving (1) and (2), we get:
`` {i}_{1}={i}_{2}=1\,\mathrm{\,A\,}``
`` ``
Potential difference between A and B:
`` {V}_{\,\mathrm{\,A\,}}-{V}_{\,\mathrm{\,B\,}}={E}_{2}-\left({i}_{1}-{i}_{2}\right)\times 1=2-\left(1-1\right)=2\,\mathrm{\,V\,}``
Current through the top branch = i2 = 1 A
Current through the middle branch = i1 - i2 = 0 A
Current through the bottom branch = i1 = 1 A
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