Question

Three resistors are connected as shown in the diagram.

Through the resistor 5 ohm, a current of 1 ampere is flowing.

(i) What is the current through the other two resistors?
(ii) What is the p.d. across AB and across AC?
(iii) What is the total resistance

Answer 1

The resistance between B and C are in parallel. Hence the total resistance, R between B and C is given by:
 R_BC= [15 x 10 ] / [ 15 + 10 ] = 6 Ω ... (a)
Potential drop across B and C = IR = 1 x 6 = 6 V
Current through the 10 Ω resistor = V / R = 6 / 10 = 0.6 A
Current through the 15 Ω resistor = V / R = 6 / 15 = 0.4 A
 p.d. across AB:
V_AB = 5 x 1 = 5 V
p.d. across AC:
V_AC = I x R_AC
R_AC = R + 5 = 11 Ω (see equation (a) )
 V_AC = 1 x 11 = 11 V
 Total resistance, R_AC = R_BC + R_AC
                                      = 6 + 5
                                      = 11 Ώ