Conversion of a Galvanometer into Ammeter and Voltmeter

Conversion of a Galvanometer into Ammeter and Voltmeter

Conversion of a Galvanometer into an Ammeter

An ammeter is an instrument used to measure the current passing through a circuit. A galvanometer can be converted into ammeter by connecting a low resistance called shunt in parallel to the galvanometer.

Let G be the resistance of the galvanometer, I be the maximum current to be measured by the ammeter, and I_g be the maximum current that can be passed through the galvanometer. Then, (I-I_g) is the current passing through the shunt, S.

Since G and S are in parallel combination,

\begin{align*} \: \text {p.d. across S} =\text {p.d. across G} \\ (I – I_g)S &= I_g G \\ S &= \frac {I_g}{I – I_g} \times G \\ \end{align*}

This is the value of shunt which is connected in parallel to the galvanometer and this connection is converted into ammeter of range (0 – I) amperes. The effective resistance R_A of the ammeter is given by

\begin{align*} \frac {1}{R_A} &= \frac {1}{G} + \frac {1}{S} \\ \text {or} \: R_A &= \frac {GS}{G + S} \\ \end{align*}

So, the resistance of ammeter is smaller than S. Since S is low resistance, resistance of ammeter R_A is very low and when it is connected in series in the circuits, it will not affect the current passing through the circuit.

Conversion of a Galvanometer into a Voltmeter

A voltmeter is a device used to measure the potential difference between two points in a circuit. A galvanometer can be converted into voltmeter by connecting a high resistance called multiplier in series to the galvanometer.

Let G be the resistance of the galvanometer and I_g, the maximum deflection in the galvanometer. To measure the maximum voltage, V by the voltmeter, the high resistance R is connected in series. So,

\begin{align*} V &= I_g (R + G) \\ \text {or,} \: I_g R &= V – I_g G \\ \text {or,} \: R &= \frac {V}{I_g} – G \\ \end{align*}

This equation gives the value of resistance R, which connected in series to the galvanometer, is converted into a voltmeter of range 0 – V volts. The effective resistance of the voltmeter R_v = R + G. since R is high, the resistance of the voltmeter R_v is high and it will not draw much current from the circuit.

Ohmmeter

An ohmmeter is an arrangement which used for measuring resistance. It consists of a meter a resistor and a source connected in series as shown in a figure. The resistance R to be measured is connected between the terminals x and y. The series R is variable, it is adjusted as that when terminals x and y are short-circuited (i.e. when R = 0), the metre deflects full-scale. When nothing is connected to terminals x and y, so that the circuit between x and y is open (i.e. when R → ∞), there is no current and no deflection. For any value of R, the meter deflection depends on the value of R, and the metre scale can be calibrated to read the resistance, so this scale reads backward compared to the scale showing the current.

Potential Divider

A potential divider is an arrangement of resistors in series across a given p.d. to provide a known fraction of the potential difference. Figure shows a potential divider with resistance R₁ and R₂ across a p.d. of V.

\begin{align*} \text {The current flowing, I in the circuit is given by} \\ I &= \frac {V}{R_1 + R_2} \\ \text {Then p.d. across,} \: R_1, V_1 = IR_1 = \frac {R_1}{R_1 + R_2} V \\ \text {The fraction of V obtained across} \: R_1 \text {is} \: \frac {R_1}{R_1 + R_2} \\ \text {If} \: R_1 = 10 \mho \text {and} \: R_2 = 90 \mho, \text {then} \: V_1 = \frac {10}{90 + 10} V = \frac {10 V}{100} = \frac {V}{10} \\ \end{align*}

A resistor with a sliding contact can be used as a potential divider as shown in the figure. This arrangement provides a continuously variable p.d. from zero to the full supply value.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.