Consider the following figure. Note: The currents are not necessarily in the dir

Question

Consider the following figure. Note: The currents are not necessarily in the direction shown. (Assume R1 = 21.0 , R2 = 2.0 , and V = 36 V.)

(a) Find the current in each resistor of the figure above by using the rules for resistors in series and parallel.

(b) Write three independent equations for the three currents using Kirchoff's laws: one with the node rule; a second using the loop rule through the battery, the 2.0- resistor, and the 24.0- resistor; and the third using the loop rule through the 21.0- and 24.0- resistors. Solve to check the answers found in part (a).

Explanation / Answer

let,

R1=21 ohms, R2=2 ohms, R3=24 ohms

V=36 v

a)

R13=R1*R3/(R1+R3)

=21*24/(21+24)

=11.2 ohms

R123=R2+R13

=2+11.2

=13.2 ohms

I123=V/R123

=36/13.2

=2.73 A

here,

I2=I13=2.73 A

V13=I13*R13

=2.73*11.2

=30.58 v

now,

I1=V13/R1=30.58/21=1.46 A

I3=V13/R3=30.58/24=1.27 A

there fore,

current through R2 is I2=2.73 A

current through R1 is I2=1.46 A

current through R3 is I3=1.27 A

b)

by using Kirchhoff's law,

I3*R3-I1*R1=0

I3*24-I1*21=0 ---(1)

and

V-I2*R2-I3*R3=0

36-I2*2-I3*24=0 --(2)

I1+I3=I2 ---(3)

from the above all three equation,

I1=1.45 A,

I2=2.73 A

I3=1.27 A

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