When you want to measure the poten- tial difference between two points on a circ

Question

When you want to measure the poten- tial difference between two points on a circuit, you connect the voltmeter be- tween these points, i.e., in parallel to the circuit. As this act changes the circuit, you alter the value that you intend to measure. This shows that a voltmeter can never measure the intended poten tial difference As an example, consider the circuit shown above. You would like to measure the potential difference Vab with a voltmeter. Let's compute this potential difference with and without a voltmeter (a) First consider the case where the voltmeter is not attached. We suppose that the internal resistance of the emf device is included in the resistor at the top, so, don't worry about that Find Vab (b) Next, consider the case when a voltmeter is attached. A voltmeter is essentially a gal- vanometer (a device that measures currents) connected in series with a resistor (resistance of which is Rs). If ig is the current that the galvanometer reads, then the value ?GRs is presented as the voltmeter's reading. We as- sume that the internal resistance of the gal- vanometer is included in Rs; as a result, do not worry about that In most voltmeters, different Rs values are used in different "maximum voltage settings". Suppose that the series resistance is Rs 40 kS2 for the setting you use Solve the currents for the circuit when the voltmeter is connected between points a and b. Find the value Va (The voltmeter will show this value to us) (c) What is the fractional error between the actual value without voltmeter and the measured value of Vab? (d) If you wanted to measure Vab much more accurately, how should you choose Rs? For example, if you wanted to measure Vab with an at most 0.1% fractional error, how should you choose Rs? Why don't the voltmeter-producers choose such resistors and make perfect voltmeters?

Explanation / Answer

(a.) Potential difference without using voltmeter,

V=(12/20)*10=6V

(b.) Potential difference on applying voltmeter,

V=(12/18)*8=5.33V

(c.) Fractional error,={(6-5.33)/6}*100=11.16%

(d.) For 0.1 % fractional error,

Voltage should be, V=5.994V

and for this much voltage , value for Rs can be calculated as-

Rs=4999.16 kohm.

For very high resistance , Sensitivity of voltmeter will be affacted and also as resitance have some tolerance then the value shown by voltmeter will vary rapidly.

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