In this example, if the emf of the 4 V battery is increased to 15 V and the rest of the circuit remains the same, what is the potential difference Vab?

The image of the circuit has been attached

At 12 emf Vab = 9.5 V

At 15 emf Vab = 12.94 V

Explanation:

Kirchhoff loop rule states that the sum of the currents coming into a junction equals the sum of the currents going out of a junction. That is to say that the sum is equal to zero.

Calculations

The voltage in a circuit can be calculated using the expression;

V= IR .............1

since the Applying Kirchhoff rule to the circuit we have;

Calculating Vab (the voltage across ab) when the emf is 12 v

let us obtain the value of the current flowing across the circuit using equation 1 and Kirchhoff loop rule

+12 - (I x 2) -(I x 3)-(I x 4)-(4)-(I x 7) = 0

I = 8/16 = 0.5 A

calculating the voltage across Vab we have;

Vab = 4V + (I x 7) + (I x 4)

Vab = 4V + (0.5 x 7) + (0.5 x 4)

Vab = 4 +3.5+2

Vab = 9.5 V

at 12v emf Vab is 9.5V

calculating Vab at 15 emf value using equation and also Kirchhoff's loop rule we have;

+15 - (I x 4) -(I x 3)-(I x 2)-(12)-(I x 7) = 0

I = 3/16

I =0.1875 A

Vab = 15 V -(I x 7) - (I x 4)

Vab = 15 - ( 0.1875 x 4)-(0.1875 x 7)

Vab = 15 - 0.75-1.3125

Vab = 12.94 V