Four resistors are connected across an ideal dc source of V = 8.0 V,as shown in the figure.Assume all resistances shown are accurate to two significant figures.What is the current through the 9.0-Ω resistor?
A)1.0 A
B)0.67 A
C)0.50 A
D)0.90 A
E)2.0 A

Question

Four resistors are connected across an ideal dc source of V = 8.0 V,as shown in the figure.Assume all resistances shown are accurate to two significant figures.What is the current through the 9.0-Ω resistor? 
A)1.0 A 
B)0.67 A 
C)0.50 A 
D)0.90 A 
E)2.0 A

Quizplus · Accepted Answer

To find the current through the 9.0-Ω resistor, we need to find the total resistance of the circuit and then use Ohm's Law.

First, we can combine resistors R2 and R3 in parallel:
1/R23 = 1/R2 + 1/R3 = 1/6.0 + 1/4.0 = 5/12
R23 = 12/5 = 2.4 Ω

Next, we can combine resistors R1 and R23 in series:
R123 = R1 + R23 = 3.0 + 2.4 = 5.4 Ω

Finally, we add resistor R4 in series:
R1234 = R123 + R4 = 5.4 + 9.0 = 14.4 Ω

Now, we can use Ohm's Law: 
V = IR
I = V/R1234 = 8.0/14.4 = 0.5556 A

So, the current through the 9.0-Ω resistor is the same as the total current:
I_9 = 0.5556 A

Round to two significant figures gives 0.56 A, which is closest to option B, 0.67 A.

Four Resistors Are Connected Across an Ideal Dc Source of V