What is the current in the circuit shown in the figure for t

What is the current in the circuit shown in the figure for the following? (Let R = 4 Ohm and V = 30 V. Calculate the total current drawn from the battery.) When the switch is open When the switch is closed

Solution

(a). When switch is open:

1 ohm ,1ohm are in series.

Resultant of these two is R \' = 1 + 1 = 2 ohm

R and R are in series.resultant of these two is R\" = R+R

                                                                       = 4 +4 = 8 ohm

R \' and R\" are in parallel.

Let the equivalent resistance br Req then ,

(1/Req) = (1/R \' )+(1/R \" )

           =(1/2) +(1/8)

           =(4+1) / 8

           = 5/8

Req = 8/5

Current in the circuit i = V /Req

                               = 30 /(8/5)

                              = 18.75 A

When switch is closed:

R and 1 ohm are in parallel.

Resultant of these two is R \' then

(1/R \') =(1/R ) +(1/1)

         =(1/4) + 1

        = (5/4)

    R \' = 4/5

similarly , other combination of R and 1 ohm

R and 1 ohm are in parallel.

Resultant of these two is R \' then

(1/R \') =(1/R ) +(1/1)

         =(1/4) + 1

        = (5/4)

    R \' = 4/5

R \' and R \' are in series.

So, ewuivalent resistance Req = R \' + R \'

                                             = (4/5)+(4/5)

                                             = 8/5

Current i = 30 volt / (8/5)

             = 18.75 A