Question

For the circuit shown in the figure, find the current through resistor R3 =6.0 Ω (the top one) and the potential difference across resistor R3=6.0 Ω (the top one)

Answer 1

we figure out the parallel circuit first

thats Rp = 10*15/(10+15)= 150/25 = 6ohms

so it's equivalent to 24 volts plus 2x 6-ohm resistors.


I used Kirchoff's VOLTAGE law which states that sum of the voltage drops in a closed-loop will be 0.
+24 volts from batter - equal voltage across two identical resisters means THE VOLTAGES MUST BE IDENTICAL SO 24/2 = 12 VOLTS ACROSS each resister.

That means 12 volts across R1 = 6 ohm
so A) is I = 12/6 = 2 amps
you could use total resistance if you like
I = Vt/Rt= 24/12 = 2 amps.. since the series circuit the 6-ohm resistor had 2 amps in it.


B) we found that to find the current so it 12 volts because the parallel circuit was 6 ohms equivalent .. so the voltage had to be spread over both equally...

If you know 2 amps.. and you know R = 6
then V = I*R = 2*6 = 12. volts drop across 6 ohm resistor

C) We know the voltage across the parallel circuit is 12 volts as stated above.
so
the current through he 15-ohm resister is
I = V/R = 12/15 = 0.8 amps

D) as stated before if the potential difference across the EQUIVALENT resister for the parallel circuit is 12 volts.. the voltage across the parallel circuit is 12 volts.
and since the 15-ohm resister connects from start to end of the parallel circuit it must be 12 volts drop.

E) since the current going in the parallel circuit is 2 amps then it must split between the branches and that means 1.2 amps goes into the 6 + 4-ohm resister combination
because 0.8 amps went through the 15-ohm resister.
The sum of I's going into a node must equal the sum of I's leaving a node.

That's Kirchoff's current law.
It = I15 + I(6+4)
2.0 = 0.8 + I(6+4)
1.2 = I (6+4) the six and 4 are the resister names
only not values to be multiplied.

The R3 = 6 ohms has 1.2 amps going through it.

F)
V = I*R = 1.2*6 = 7.2 volts.

G) since 4ohm resister in series with 6 ohm it has the same current
I = 1.2 amps

H) V = I * R = 1.2*4 = 4.8 volts.

I hope that helped show you how to solve future ones always try and change the circuit to an easier to see configuration.


Oh to check the voltages across the 6 and 4 ohm in the parallel circuit they should add up to 12 V

V6 + V4 = 7.2 + 4.8 = 12volts checked ok
ps V6 = voltage on the 6 ohm resister
and V4 = voltage on the 4 ohm