When four identical resistors are connected to an ideal battery of voltage V = 10 V as shown in the figure, the current I is equal to 0.20 A. What is the value of the resistance R of the resistors?
A) 20 Ω
B) 40 Ω
C) 30 Ω
D) 50 Ω
E) 10 Ω

Question

When four identical resistors are connected to an ideal battery of voltage V = 10 V as shown in the figure, the current I is equal to 0.20 A. What is the value of the resistance R of the resistors? 
A) 20 Ω 
B) 40 Ω 
C) 30 Ω 
D) 50 Ω 
E) 10 Ω

Quizplus · Accepted Answer

Using Ohm's Law, V = IR, we can solve for the resistance of each resistor: 
V = IR 
10 V = (0.20 A)(R) 
R = 50 Ω

However, since we have four resistors in parallel, the total resistance will be smaller. In a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances:

1/R(total) = 1/R + 1/R + 1/R + 1/R
1/R(total) = 4/R
R(total) = R/4

We know that I = V/R(total) = 0.20 A, and V = 10 V, so

0.20 A = 10 V / (R/4)
R/4 = 50 Ω 
R = 200 Ω / 4 
R = 50 Ω

Therefore, the value of the resistance of each resistor is 50 Ω, which is answer choice D.

When Four Identical Resistors Are Connected to an Ideal Battery