Question

(a) Three resistors 2 W, 4 W and 5 W are combined in parallel. Whatis the total resistance of the combination? (b) If the combination is connected to a battery of emf 20 V andnegligible internal resistance, determine the current througheach resistor, and the total current drawn from the battery.

Answer 1

(a)

It is given that there are three resistors of 2Ω, 4Ω and 5Ω resistance combined

in parallel.

The total resistance for the parallel combination of resistances is,

1 R = 1 R 1 + 1 R 2 + 1 R 3

Substitute the values.

1 R = 1 2 + 1 4 + 1 5 1 R = 19 20 R= 20 19 Ω

Thus, the value of total resistance is 20 19 Ω.

(b)

It is given that the battery has an emf of 20V.

The current through resistor R 1 is,

I 1 = V R 1

Substitute the value of V and R 1 in the above equation.

I 1 = 20 2 I 1 =10 A

The current through resistor R 2 is,

I 2 = V R 2

Substitute the values.

I 2 = 20 4 I 2 =5 A

The current through resistor R 3 is

I 3 = V R 3

Substitute the values.

I 3 = 20 5 I 3 =4 A

Total current in the circuit is,

I= I 1 + I 2 + I 3 I=10+5+4 I=19A

Thus, the value of current through resistors is 10A, 5A and 4A and the total current in the circuit is 19A.