FIGURE 21-15
-Four resistors of values 2.0 Ω, 4.0 Ω, 3.0 Ω, and 9.0 Ω are connected across a DC source with voltage V as shown in Figure 21-15. If the total current through this circuit is 2.0 A, what is the current through the 4-Ω resistor?
A) 1.0 A
B) 2.0 A
C) 3.0 A
D) 1.3 A
E) 2.4 A

Question

FIGURE 21-15 
-Four resistors of values 2.0 Ω, 4.0 Ω, 3.0 Ω, and 9.0 Ω are connected across a DC source with voltage V as shown in Figure 21-15. If the total current through this circuit is 2.0 A, what is the current through the 4-Ω resistor?
A) 1.0 A 
B) 2.0 A 
C) 3.0 A 
D) 1.3 A 
E) 2.4 A

Quizplus · Accepted Answer

To find the current through the 4-Ω resistor, we first need to calculate the total resistance of the circuit. Using Ohm's law, we know that V=IR, where V is the voltage, I is the current, and R is the resistance. Rearranging this equation, we get R=V/I. The total resistance of the circuit is therefore:

R_total = 2.0 Ω + 4.0 Ω + 3.0 Ω + 9.0 Ω = 18.0 Ω

Using Ohm's law again, we can find the current through the 4-Ω resistor:

I_4Ω = V/R_4Ω

We don't know the voltage, but we do know the total current through the circuit, which is:

I_total = I_2Ω + I_4Ω + I_3Ω + I_9Ω

Substituting the appropriate resistances and rearranging, we get:

I_4Ω = I_total - I_2Ω - I_3Ω - I_9Ω

To find the currents through the other resistors, we can use Ohm's law again:

I_2Ω = V/R_2Ω
I_3Ω = V/R_3Ω
I_9Ω = V/R_9Ω

Since all the resistors are in parallel, they all have the same voltage, so we can set these three equations equal to each other to get:

I_2ΩR_2Ω = I_3ΩR_3Ω = I_9ΩR_9Ω

Using this, we can solve for the current through each resistor:

I_2Ω = I_total * R_2Ω / R_total = 2.0 A * 2.0 Ω / 18.0 Ω = 0.22 A
I_3Ω = I_total * R_3Ω / R_total = 2.0 A * 3.0 Ω / 18.0 Ω = 0.33 A
I_9Ω = I_total * R_9Ω / R_total = 2.0 A * 9.0 Ω / 18.0 Ω = 1.0 A

Now we can substitute these values into the equation for I_4Ω:

I_4Ω = I_total - I_2Ω - I_3Ω - I_9Ω = 2.0 A - 0.22 A - 0.33 A - 1.0 A = 0.45 A

Therefore, the current through the 4-Ω resistor is 0.45 A, or 1.3 A rounded to one significant figure. The correct answer is D).

FIGURE 21-15 -Four Resistors of Values 2.0 Ω, 4.0 Ω, 3.0 Ω