Consider the circuit shown in the figure(Figure 1). Suppose the four resistors i
ID: 581642 • Letter: C
Question
Consider the circuit shown in the figure(Figure 1). Suppose the four resistors in this circuit have the values R_1 = 11 ohm, R_2 = 7.0 ohm, R_3 = 6.5 ohm, and R_4 = 13 ohm, and that the emf of the battery is epsilon = 18 V. 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.Explanation / Answer
As I look at the circuit, I see that R2 and R4 are parallel to R3.
R2 + R4 = 7 + 13 = 20
Now let’s determine the equivalent resistance of the parallel circuit.
1/Req = 1/20+ 1/6.5 = 6.9/120.06 + 17.4/120.06 = 24.3/120.06
Req = 120.06/24.3
This is approximately 4.9056 . To determine the total resistance, add R1.
Total R = 120.06/24.3 + 13
This is approximately 17.94074
Total current = 18 ÷ (120.06/24.3 + 13) = 1.003303055 amps
All of the current flows through R1
V = 13 * 1.003303055 = 13.042993972
18 – 13.042993972 = 4.957060285
This is the voltage for the parallel circuit.
For R3, V = I * R
4.957060285 = 6.9 * I
I = 4.957060285 ÷ 6.9 = 0.718414534 amps
For R2 and R 4:
4.957060285 = 17.4 * I
I = 4.957060285 ÷ 17.4 = 0.284888522 amps
0.718415344 + 0.284888522 = 1.00330056
This proves that the currents are correct.
For R1, I = 1.003303055 amps
For R3, I = 0.718414534 amps
For R2 and R4, I = 0.284888522 amps