Three parallel-connected resistors when connected across a DC voltage source dissipate a total power of 72 W. The total current drawn is 6 A.

Three parallel-connected resistors when connected across a DC voltage source
dissipate a total power of 72 W. The total current drawn is 6 A. The current flowing through
the first resistor is 3 A and the second and third resistors have equal values. What are the
resistances of the three resistors? Draw the figure.

 

[anisingh259]

Let the total resistance is Req and dc voltage is V voltage and total current be I amp then.
Total power P = 72W and I = 6A
V*I = 72
Then V = 12V
Current through first resistor is I1 3A let it resistance is R1 then.
12/R1 = 3
R1= 4
Let second resistance is R2 and current flowing through it is I_2
And third resistance is R3 and current flowing through it is I_3
If second and third resistor have equal value, then equal current will flow through them.
R2 = R3 and I2 = I3
I = I_1 + I_2 + I_3 = I_1 + 2I_2
6 = 3 + 2I_2
I_2 = 3/2
So R2 = V/I2 = 12/1.5 = 8 ohm
So R3 = R2 = 8 ohm