An equivalent resistance of 3.0 ohm is produced by combining an unknown resistor R and a 4 ohm resistor. What is the value of R and how is it connected to the 4 ohm resistor?
A. 2.4 ohm parallel
B. 2.4 ohm series
C. 12.0 ohm parallel
D. 12.0 ohm series
I need your guidance in this question. I'm having a hard time on how to solve this one step-by-step.
clearly the two resistors are not connected in series (why?)
That means they are connected in parallel.
So now you just need to find R such that
1/4 + 1/R = 1/3
Better review series/parallel resitances
To determine the value of resistor R and its connection to the 4 ohm resistor, we need to use the concept of equivalent resistance. Equivalent resistance is the total resistance experienced by the circuit when multiple resistors are combined.
When resistors are connected in series, their resistances add up, while when they are connected in parallel, the reciprocal of their resistances add up.
In this case, the unknown resistor R and the 4 ohm resistor are combined to produce an equivalent resistance of 3.0 ohm.
Let's consider the possible options:
A. 2.4 ohm parallel:
If R and the 4 ohm resistor were connected in parallel, the equivalent resistance would be given by the formula:
1/Requivalent = 1/R + 1/4
Simplifying this equation, we get:
1/Requivalent = (4+R)/4R
Solving for Requivalent, we get:
Requivalent = 4R/(4+R)
Using this formula, we can substitute the values given:
3.0 = 4R/(4+R)
By solving this equation, we find that R is equal to approximately 1.714 ohm. Since this doesn't match the given options, we can conclude that option A is incorrect.
B. 2.4 ohm series:
If R and the 4 ohm resistor were connected in series, their resistances would simply add up:
Requivalent = R + 4
Since the given equivalent resistance is 3.0 ohm, this contradicts option B. Therefore, option B is incorrect.
C. 12.0 ohm parallel:
Using the same formula mentioned previously, we can substitute the given values:
3.0 = 4R/(4+R)
By solving this equation, we find that R is equal to 2.4 ohm. This matches the value given in option C, so option C is the correct answer.
D. 12.0 ohm series:
Calculating the equivalent resistance when resistors are connected in series:
Requivalent = R + 4
Since the given equivalent resistance is 3.0 ohm, this contradicts option D. Therefore, option D is incorrect.
In conclusion, the correct answer is option C. The unknown resistor R has a value of 2.4 ohm, and it is connected in parallel with the 4 ohm resistor.