If voltage in a circuit is constant, the current can be cut to half of its original value by changing the resistance to
its original value.
Which best completes the statement?
A. one-fourth
B. one-half
C. two times
D. four times
Answer (1)
Ohm's Law states V = I R .
Since voltage is constant, I 1 R 1 = I 2 R 2 .
Given I 2 = 2 1 I 1 , then R 2 = 2 R 1 .
The resistance must be two times its original value: tw o t im es .
Explanation
Problem Analysis We are given that the voltage in a circuit is constant. We want to determine how the resistance must change to reduce the current to half of its original value. We will use Ohm's Law to solve this problem.
Applying Ohm's Law Ohm's Law states that voltage (V) is equal to the product of current (I) and resistance (R): V = I × R Since the voltage is constant, we can write: V = I 1 × R 1 = I 2 × R 2 where I 1 and R 1 are the original current and resistance, and I 2 and R 2 are the new current and resistance.
Substituting the New Current We are given that the current is reduced to half of its original value, so I 2 = 2 1 I 1 . Substituting this into the equation, we get: I 1 × R 1 = ( 2 1 I 1 ) × R 2
Solving for the New Resistance Now, we solve for R 2 in terms of R 1 :
R 2 = 2 1 I 1 I 1 × R 1 = 2 × R 1 This means the resistance must be two times its original value to reduce the current to half its original value while keeping the voltage constant.
Final Answer Therefore, the resistance should be changed to two times its original value.
Examples
In electrical engineering, Ohm's Law is fundamental for designing circuits. For example, if you want to reduce the current flowing through an LED to prevent it from burning out while maintaining the same voltage, you need to increase the resistance. If you halve the current, you double the resistance. This principle is used in adjusting volume controls in audio systems or setting the brightness of lights.
