In the circuit diagram given in (Fig. 3.57), calculate :
(a) the current through each resistor
(b) the total current in the circuit
( c) the total effective resistance of the circuit.
.

Explanation

(a) Current through `2 Omega` resistor, `I_1 = (6 V)/(2 Omega) = 3 A` , Current through `5 Omega` resistor, `I_2 = (6 V)/(5 Omega) = 1.2 A`
Current through `10 Omega` resistor, `I_3 = (6 V)/(10 Omega) = 0.6 A`
(b) Total current, `I = I_1 + I_2+I_3+I_4 = 3 A + 1.2 A +0.6 A = 4.8 A`
`I = I_1+I_2 +I_3 = 3 A + 1.2 A + 0.6 A = 4.8 A`
(c) Total resistance in the circuits is given by `(1)/(R_P) = (1)/(2)+(1)/(5)+(1)/(10)=(10 + 4 + 2)/(20) = (16)/(20)` or `R_P = 1.25 Omega`
`I = (V)/(R_P) = (6 V)/(1.25 Omega) = 4.8 A`.