Three resistors of 10.0 W, 20.0 W, and 25.0 W are connected in parallel across a 100-V battery. What is the equivalent resistance of the circuit and the current flowing through the 10.0-W resistor?

Question

anonymous · Answer

change the watt ratings to ohms for the resistors:
10w = 100V * amp
I= amp = 0.1
P = I^2 * R
10w = (0.1)^2 *R 
R 1 = 1000 ohm

20w = 100V * I 
I = 0.2 amp
20w = (0.2)^2*  R2
R2 = 500 ohm

25w = 100V *I
I = (0.25)^2 * R3
R3 = 400 ohm 

For parallel resistors:

1 / R eqiv = 1/ R1 + 1/R2 + 1/ R3
1 / R eqiv = 1 / 1000 + 1/ 500 + 1/ 400
R equivalence = 2000 / 11 = 182 ohms

The current flowing through the 10.0-W resistor?
10w = 1000 ohm
V = IR
100V = I * 1000 ohm
I = 0.1 amp current thru 10 watt resistor

radar · Answer

There are many ways to get these two things (equivalent resistance, and current through the 10 watt resistor.

For the equivalent resistance.  Total power is 10 + 20 + 25 watts or 55 watts
P = (E^2)/R   or 55=(100^2)/R  Solving for R:  R=(100^2)/55 = 181.81818 or 181.2 Ohms

The second thing current thru the 10 W resistor.
P=EI
10 = 100 I or I = 10/100 =.1 amps

radar · Answer

The solution by biire2u is correct and done in a very good step by step manner.  I just wanted to show that it was unnecessary to solve for the individual resistances in order to solve this problem.