Four resistors are connected in series such that their total resistance is 50 - if the resistance of three resistors is 5 - 10 - and 15 - respectively- find the resistance of the fourth resistor-

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Question

Four resistors are connected in series such that their total resistance is $50 Ω$ . if the resistance of three resistors is $5 Ω$ , $10 Ω$ and $15 Ω$ respectively, find the resistance of the fourth resistor.

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Solution

Step 1 - Given data and formula
The resistance of the first resistor $R_{1} = 5 Ω$
The resistance of the second resistor $R_{2} = 10 Ω$
The resistance of the third resistor $R_{3} = 15 Ω$
The total resistance of the connection $R_{s} = 50 Ω$
Consider that the resistance of the fourth resistor is $R_{4}$ .
The formula for the total resistance for series connection is
$R_{s} = R_{1} + R_{2} + R_{3} + R_{4}$
Step 2 - Finding the formula for the resistance of the fourth resistor
Rearrange the above formula.
$R_{s} = R_{1} + R_{2} + R_{3} + R_{4} R_{4} = R_{s} - R_{1} - R_{2} - R_{3}$
Step 3 - Finding the resistance of the fourth resistor
Substitute the values into the above formula to calculate $R_{4}$ .
$R_{4} = R_{s} - R_{1} - R_{2} - R_{3} R_{4} = 50 Ω - 5 Ω - 10 Ω - 15 Ω R_{4} = 20 Ω$
Hence, the resistance of the fourth resistor is $20 Ω$ .

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Four resistors are connected in series such that their total resistance is 50Ω. if the resistance of three resistors is 5Ω, 10Ω and 15Ω respectively, find the resistance of the fourth resistor.

Four resistors are connected in series such that their total resistance is $50 Ω$ . if the resistance of three resistors is $5 Ω$ , $10 Ω$ and $15 Ω$ respectively, find the resistance of the fourth resistor.