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, we can find the resistance of each resistor using the given information: 
V = IR, where V = 10 V and I = 0.20 A 
R = V/I 
R = 10 V / 0.20 A 
R = 50 Ω 
Since there are four identical resistors in parallel, we can find the equivalent resistance by using the formula: 
1/Req = 1/R + 1/R + 1/R + 1/R 
1/Req = 4/R 
Req = R/4 
Substituting the known value of R: 
Req = 50 Ω / 4 
Req = 12.5 Ω 
However, this is the equivalent resistance for the entire circuit. We want the resistance value for each individual resistor, so we divide by the number of resistors: 
R = Req / 4 
R = 12.5 Ω / 4 
R = 3.125 Ω 
Therefore, the closest answer choice is C) 30 Ω. This is because four 30 Ω resistors in parallel would have an equivalent resistance of 7.5 Ω, which is slightly lower than the calculated value of 12.5 Ω. It is also common for resistors to come in standard values, and 30 Ω is one of them.

When Four Identical Resistors Are Connected to an Ideal Battery