Question

A voltmeter having a sensitivity of 1200Q/V and read 100V on it's 220V scale when connected across an unknown resistor in series with a milliameter when the millimeter read 5mA calculate
(i) the apparent resistance of the unknown resistor.
(ii) the actual resistance of the unknown resistor.
(iii) the error due to the loading effect of the meter.

Answer 1

What we have here: a voltmeter with sensitivity 1200 ohm/volt, with scale with maximum 220 V, which shows 100 V. We know that the real current is 5 mA. How are all they connected? Assume like this:

Calculate the resistance of the voltmeter on its 220 V range:

$$R_V=1200\cdot220=264000\space\Omega.$$

(i) The apparent resistance (with an assumption that the voltmeter's resistance is infinity):

$$R_A=\frac{100}{0.005}=20000\space\Omega.$$

(ii) Find the actual resistance. 5 mA is the common current:

$$0.005=\frac{V(R_V+R_x)}{R_VR_x}=\frac{V(264000+R_x)}{264000R_x},\\ \space\\ R_x=21639.3\space\Omega.$$

(iii) The error is:

$$\Delta=\frac{|20000-21639.3|}{21639.3}\cdot100\%=7.6\%.$$