Question

In measuring a voltage, a voltmeter uses some current from the circuit. Consequently, the voltage measured is only an approximation to the voltage present when the voltmeter is not connected. Consider a circuit consisting of two 2260-Ω resistors connected in series across a 50.0-V battery. (a) Find the voltage across one of the resistors. (b) A voltmeter has a full-scale voltage of 50.0 V and uses a galvanometer with a full-scale deflection of 4.59 mA. Determine the voltage that this voltmeter registers when it is connected across the resistor used in part (a).

Answer 1

a)

$R=2260+2260=4520(\Omega)$

$I=50/4520=0.01106\ (A)$

$V=I\cdot R=0.01106\cdot4520=25\ (V)$

b)

The resistance of the galvanometer circuit is $R_G=50/0.00459=10893\ (\Omega)$

In this case the current in the circuit is $I=\frac{V}{R+R||R_G}$

$R||R_G=\frac{2260\cdot10896}{2260+10896}=1872\ (\Omega)$

$I=\frac{V}{R+R||R_G}=I=\frac{50}{2260+1872}=0.0121\ (A)$

$V_G=I\cdot R||R_G=0.0121\cdot1872=22.7\ (V)$ . Answer