Question

The current in a circuit is measured as 235 μA and the accuracy of measurement is ± 0.5%. This current is passes through a resistor 35 kΩ ± 0.2%. The voltage is estimated to be 8.23 V. The error in the estimation would be
1. ± 0.06 V
2. ± 0.04 V
3. ± 0.016 V
4. ± 0.1 V

Answer 1

Correct Answer - Option 1 : ± 0.06 V

Concept:

Limiting error:

• The maximum allowable error in the measurement is specified in terms of true value, is known as limiting error.
• It will give a range of errors. It is always with respect to the true value, so it is a variable error.
• If two quantities are getting added, then their limiting errors also gets added.
• If two quantities are getting multiplied or divided, then their percentage limiting errors get added.

 

Calculation:

Given that, current (I) = 235 μA ± 0.5%

Resistance (R) = 35 kΩ ± 0.2%

Voltage (V) = 8.23 V

From Ohm’s law,

V = IR

As, the quantities are getting multiplied, their percentage of errors get added.

Error in the measurement of voltage = 0.5 + 0.2 = ± 0.7%

The error in the measurement of voltage in volts is

\( = \frac{{0.7}}{{100}} \times 8.23 = 0.057 \approx 0.06\;V\)