Four resistors are connected across an ideal dc battery with voltage V as shown in the figure.Assume that all quantities shown are accurate to two significant figures.If the total current through this circuit is I = 2.0 A,what is the current through the 4.0-Ω resistor?
A)1.0 A
B)2.0 A
C)3.0 A
D)1.3 A
E)2.4 A

Question

Four resistors are connected across an ideal dc battery with voltage V as shown in the figure.Assume that all quantities shown are accurate to two significant figures.If the total current through this circuit is I = 2.0 A,what is the current through the 4.0-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

First, we can find the total resistance of the circuit using the formula:
Rtotal = R1 + R2 + R3 || R4 (where || denotes parallel resistance)
Rtotal = 10Ω + 20Ω + (30Ω || 4Ω)
Rtotal = 10Ω + 20Ω + 2.86Ω
Rtotal = 32.86Ω

Then, we can use Ohm's Law to find the voltage drop across the 4Ω resistor:
V = IR
V = (2.0 A)(4Ω)
V = 8.0 V

Next, we can use this voltage and the resistance of the 4Ω resistor to find the current through it:
I = V/R
I = (8.0 V)/(4Ω)
I = 2.0 A

Therefore, the current through the 4.0Ω resistor is 2.0 A, choice (D).

Four Resistors Are Connected Across an Ideal Dc Battery with Voltage