Question

3.) We consider a circuit that consists of one battery with unknown voltage (‘EMF’) E, two unknown resistors R1 and R2, and the known resistor R3 = 56Ω. The currents through the three resistors (I1, I2, and I3) are not known. The power dissipated in the three resistors are P1 = 27W, P2 = 51W, and P3 = 42W, respectively.
a) Find the ratio of the currents through the resistors R2 and R3, I2/I3!
b) Find the resistor R2!
c) Find the resistor R1! Hint: Consider the equivalent resistor of R2 and R3.
d) Find the currents through the three resistors!
e) Find the voltage [‘EMF’] of the battery!

Answer 1

As the currents through all the resistors are different so the resistors are in parallel combination.

P3= 42 W

=> E²/R3 = 42

=> E² = 42×56

=> E = 48.5 Volt (approx)

Again, P3 = E × I3

=> 42= 48.5 × I3

=> I3 = 0.866 Amp

P2 = E× I2

=> I2 = (51/48.5)

=> I2 = 1.05 Amp

Again,

P2= E²/R2

=> R2 = (48.5²/51) = 46.12

Now,

P1 = E²/R1

=> R1 = (48.5²/27) = 87.12

Again, P1= E× I1

=> I1 = (27/48.5) = 0.5567 Amp

a) ratio of I2 and I3 = (1.05/0.866) = 1.214

b) Resistor R2 = 46.12

c) Resistor R1 = 87.12

d) I1 =0.5567 Amp

I2 = 1.05 Amp

I3 = 0.866 Amp

e) Voltage of the battery = 48.5 V