Question

The potential difference between A and B in the following situation is

Answer 1

Answer:

12 V

Explanation:

Let us rename given circuit.

From the renamed circuit, we can clearly see that at point B, 3 A current flow to C and 4 A current flows to point E. This means total outgoing current at point B is 7 A. According to the junction rule, current at junction B must be zero. So, incoming current at junction B must be 7 A. Therefore, 7 A current comes from point F to point B.

Now, using the Ohm's law, we have

$V_A - 2\times 5+10-1\times 7 -5=V_B\\\Rightarrow V_A-10+10-7-5=V_B\\\Rightarrow V_A-12=V_B\\\Rightarrow V_A-V_B=12\\\Rightarrow \Delta V = 12$

This means the potential difference between point A and B is 12 V.

Answer 2

Answer:

(1) 12 v

Explanation:

Let the junction after 10V battery be F.

from A to F, p.d is

Va - 2x5 + 10= Vf

(acg to sign convention, since we are going in direction of circuit and crossing a resistor, therefore, potential=IR is -ve. and since we are crossing the battery from -ve to +ve terminal, it's potential will be +ve)

Va - Vf =0 (1)

so we can say potential from Va to Vf is 0 and won't contribute in final potential.

At junction B, you can see current splitting into 3 and 4 amperes for a total of 7A. Incoming current must be equal to outgoing current. therefore Current coming from Pt D is 2A.

Now from Junction F to Junction B

Vf - 7x1 - 5=Vb

(Since, we are going in direction of current, therefore, potential= IR of resistor will be -ve. And since we are crossing the battery from +ve to -ve terminal, the potential of battery will be -ve)

Vf - Vb = 12V (2)

adding (1) and (2)

Va -Vf + Vf -Vb = 0 + 12

Va-Vb=12V