
A resistance of with tolerance 10% and another of with tolerance 10% are connected in series. The tolerance of combination is about
A. 5%
B. 10%
C. 12%
D. 15%
Answer
502.5k+ views
Hint: In series, the equivalent resistance of two resistors increases as it is the sum of resistances. The tolerance of the equivalent resistance in series is the ratio of total error in the measurement of resistance to the equivalent resistance.
Formula Used:
The equivalent resistance of the series combination of two resistors of resistance and is,
The tolerance of the resistance is given as,
Here, R is the resistance and is the error in the resistance.
Complete step by step answer:
We express the resistance of the resistor in terms of its error as follows,
.
And, .
We can express the equivalent resistance of series combination of and as follows,
Now we have to calculate the percentage of tolerance of the equivalence resistance as below,
…… (1)
We have, the tolerance of resistance is,
And,
We can substitute , , and in equation (1).
Therefore, the percentage tolerance in series is 10%.
Therefore, the correct answer is option (B).
Note:The tolerance is the error in the measurement of the resistance. It is always given in percentage. To calculate the tolerance, divide the error in the measurement of resistance by the given resistance. In series, the resistance of the circuit increases while in parallel combination of resistors, the equivalent resistance decreases.
Formula Used:
The equivalent resistance of the series combination of two resistors of resistance
The tolerance of the resistance is given as,
Here, R is the resistance and
Complete step by step answer:
We express the resistance of the resistor in terms of its error as follows,
And,
We can express the equivalent resistance of series combination of
Now we have to calculate the percentage of tolerance of the equivalence resistance as below,
We have, the tolerance of resistance
And,
We can substitute
Therefore, the percentage tolerance in series is 10%.
Therefore, the correct answer is option (B).
Note:The tolerance is the error in the measurement of the resistance. It is always given in percentage. To calculate the tolerance, divide the error in the measurement of resistance by the given resistance. In series, the resistance of the circuit increases while in parallel combination of resistors, the equivalent resistance decreases.
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