c For the circuit shown in the figure determine the current

(c) For the circuit shown in the figure, determine the current in the 4.0-? resistor.

Solution

3 ohm ,4 ohm,5 ohm are in parallel.

Let the resultant of these three be R then,

(1/R)=(1/3)+(1/4)+(1/5)

       = 0.7833

   R = 1.276 ohm

R , 2 ohm,1 ohm are in series.

So, equivalent resistance of the circuit R \' = R + 2 + 1

                                                            = 1.276 + 3

                                                            = 4.276 ohm

Potential difference V = 12 volt

Current through the circuit i = V/R \'

                                        = 12/4.276

                                        = 2.806 A

The ratio of Currents in 3 ohm,4 ohm,5 ohm is

   i1:i2:i3 = (1/3):(1/4):(1/5)

             = (60/3):(60/4):(60/5)

             = 20 :15:12

Therefore current in 3 ohm resistor i1 = i[20/(20+15+12)]

                                                       =2.806 [20/47]

                                                       = 1.194 A

current in 4 ohm resistor i1 = i[15/(20+15+12)]

                                       =2.806 [15/47]

                                      = 0.8955 A