Find the current in each resistor and the voltage difference between points a and b. Let emf1 = 6.0 V, emf2 = 5.0 V, emf3 = 4.0 V, R1 = 100 ohm, and R2 = 50 ohm.
Also, what is the current through emf2?
Which resistor is dissipating more power?
Although the full approach relying on solution of simultaneous equations is not required, it is not a bad idea to follow some of the suggestions for solving multiloop equations. That is, pick current directions and label circuit accordingly.
By inspection, we notice that R1 is in parallel with a "perfect" emf2. Ohm's law may thus be readily applied to yield the current in R1 of emf2 / R1 = 5 V / 100 ohm = 50 mA.
For the current in R2, it is best to apply the loop rule. From that, you would find that the effective emf experienced by R2 is emf2 - emf1 + emf3. Thus the current in R2 is (5-6+4 V) / 50 ohm = 3 V / 50 ohm = 60 mA.
The voltage difference between a and b is best seen from the original figure to be emf3 + emf2 = 9.0 V.
Applying the junction rule to either of the two junctions shows that the current in emf2 is the sum of the current in R1 and R2 which is 110 mA.
The power dissipated by R1 is (50 mA)(5 V) = 250 mW.
The power dissipated by R2 is (60 mA)(3 V) = 180 mW.
R1 is dissipating more power than R2.
|emf1||(110 mA)(5 V)||= 550 mW||delivered|
|emf2||(60 mA)(6 V)||= 360 mW||absorbed|
|emf3||(60 mA)(4 V)||= 240 mW||delivered|
|total||(550 - 360 + 240) mW||= 430 mW||as expected|