Question

A. Write Kirchhoff's loop rule (clockwise) for the circuit shown in (Figure 1).

B. Determine the current in the circuit for the case in which ε1 = 20.0 V, ε2 = 8.0 V, R1 = 30.0 Ω, R2 = 20.0 Ω, and R3 = 10.0 Ω.

C. Using this value of current, start at position A and move clockwise around the circuit, calculating the electric potential change across each element in the circuit (be sure to indicate the sign of each change). Find the electric potential change across R1.

D. Find the electric potential change across ε1.

E. Find the electric potential change across R3.

F. Find the electric potential change across ε2.

G. Find the electric potential change across R2.

H. Add these potential changes around the whole circuit.

Answer 1

a)

Applying Kirchoff's loop rule

Applying Kirchoff's loop rule Epsilon_1 - IR_3 - epsilon_2 - IR_2 - IR_1 = 0 b) epilon_1 - IR_3 - epsilon_2 - IR_2 - IR_1 = 0 I = (epsilon_1 - epsilon_2)/(R_1 = R_2 + R_3) I = (20-8)/(30 + 20 + 10) = 0.2 A c) V_1 = -IR_1 = -0.2*30 = -6 V d) V_E1 = E_1 = 20 V e) V_3 = -IR_3 = -0.2*10 = -2 V f) V_E2 = -E_2 = -8 V g) V_2 = -IR_2 = -0.2*20 = -4 V h) adding all potential = -6 + 20-2-8-4 = 0 V

b)

I=(20-8)/(30+20+10) =0.2 A

c)

V₁=-IR₁=-0.2*30 =-6 V

d)

V_E1=E₁=20 V

e)

V₃=-IR₃=-0.2*10 =-2 V

f)

V_E2=-E₂=-8 V

g)

V₂=-IR₂=-0.2*20 =-4 V

h)

adding all potential

=-6+20-2-8-4 =0 V