Question

 For the circuit shown in the figure, calculate the following. (Assume ε = 8.40 V and R = 5.94 Ω.) 

 (a) the current in the 2.00-12 resistor (Enter the magnitude.)

 (b) the potential difference between points a and b, ΔV = Vb - Va

Answer 1

here,

E = 8.4 V

R = 5.94 ohm

a)

let the current through 12 V be i1 and E be i2

using KVL in the upper loop

4 * i1 + 2 * ( i1 - i2) = 12 .....(1)

and

using KVL in the lower loop

R * i2 - 2 * ( i1 - i2) = E

5.94 * i2 - 2 * ( i1 - i2) = 8.4 .....(2)

from (1) and (2)

i1 = 2.57 A

i2 = 1.7 A

a)

the current through 2 ohm , I = i1 - i2

I = 2.57 A - 1.7 A = 0.87 A

b)

the potential difference between A and B , V = 2 * I

V = 2 * 0.87 V = 1.74 V