Respuesta :
Answer:
15 ohms
Explanation:
- The effective resistance of resistors is calculated depending on whether the resistors are arranged in series or parallel.
- The effective resistances of resistors in parallel is calculated using the formula;
[tex]\frac{1}{Rt}=\frac{1}{R1}+\frac{1}{R2}+\frac{1}{R3}+.......\frac{1}{Rn}[/tex]
In this case we are given,
Effective resistance, Rt as 5.0 Ω
First resistor has 10 Ω
second resistor has 30 Ω
We are required to calculate the resistance of the third resistor;
But, effective resistance for parallel arrangement is given by;
[tex]\frac{1}{Rt}=\frac{1}{R1}+\frac{1}{R2}+\frac{1}{R3}+.......\frac{1}{Rn}[/tex]
Then;
[tex]\frac{1}{5}=\frac{1}{10}+\frac{1}{30}+\frac{1}{R3}[/tex]
[tex]\frac{1}{5}=\frac{2}{15}+\frac{1}{R3}[/tex]
Thus;
[tex]\frac{1}{R3}=\frac{1}{5}+\frac{2}{15}[/tex]
[tex]\frac{1}{R3}=\frac{1}{15}[/tex]
Therefore;
[tex]R3 = 15ohms[/tex]
Thus, the resistance of the third resistor is 15 ohms
The resistance of the third resistor is 15 ohms
Equivalence of Resistors
From the question, we are to determine the resistance of the third resistor
For three resistors in parallel, the equivalent resistance is given by
[tex]\frac{1}{R_{eq} } = \frac{1}{R_{1} } + \frac{1}{R_{2} } + \frac{1}{R_{3} }[/tex]
From the given information,
[tex]R_{eq} = 5.0 \ ohms[/tex]
[tex]R_{1} = 10.0 \ ohms[/tex]
[tex]R_{2} = 30.0 \ ohms[/tex]
Putting the parameters into the formula, to determine [tex]R_{3}[/tex]
That is,
[tex]\frac{1}{5.0} = \frac{1}{10}+\frac{1}{30} +\frac{1}{R_{3} }[/tex]
Then,
[tex]\frac{1}{5.0} - \frac{1}{10}+\frac{1}{30} = \frac{1}{R_{3} }[/tex]
[tex]\frac{6-3+1}{30} = \frac{1}{R_{3} }[/tex]
[tex]\frac{2}{30} = \frac{1}{R_{3} }[/tex]
[tex]\frac{1}{15} = \frac{1}{R_{3} }[/tex]
∴ [tex]R_{3} =15 \ ohms[/tex]
Hence, the resistance of the third resistor is 15 ohms
Learn more on Equivalence of Resistors here: https://brainly.com/question/469388
