Question

Consider the circuit shown in the figure(Figure 1). Suppose the four resistors in this circuit have the values R1 = 13 Ω , R2 = 7.2 Ω , R3 = 6.9 Ω , and R4 = 11 Ω , and that the emf of the battery is E = 15 V . You may want to review (Pages 748 - 751) . Find the current through each resistor using the rules for series and parallel resistors. Express your answers using two significant figures separated by commas. Find the current through each resistor using Kirchhoff's rules. Express your answers using two significant figures separated by commas.

Answer 1

From the circuit, we can see that R2 and R4 are parallel to R3.

R2 + R4 = 7.2 + 11 = 18.2 Ω

Now, determine the equivalent resistance of the parallel circuit.

1/Req = 1/18.2 + 1/6.9 = 0.19987

=> Req = 5.0 Ω .

Now to determine the total resistance, add R1.

Total R = 5.0 + 13 = 18.0 Ω

So, total current = 15 ÷ 18.0 = 0.833 A

All of the current flows through R1
V = 13 * 0.833 = 10.83 V
15.0 – 10.83 = 4.17  
This is the voltage for the parallel circuit.

For R3, V = I * R
4.17 = 6.9 * I
I = 4.17 / 6.9 = 0.60 A

For R2 and R 4:
4.17 = 18.2 * I
=> I = 4.17 / 18.2 = 0.23 A

0.60 + 0.23 = 0.83 A
This proves that the currents are correct.

Therefore -

For R1, I = 0.833 A
For R3, I = 0.60 A
For R2 and R4, I = 0.23 A