( a ) Voltmeter: -
Voltmeter is used to measure the potential difference between any two points of a circuit.
Galvanometer with suitable modification is used for this purpose. However, there are two practical difficulties in using galvanometer as a voltmeter:
( 1 ) To measure potential difference across a circuit element, galvanometer has to be connected in parallel to it. This alters the resistance of the circuit and the current flowing through the circuit element and hence the potential difference across it.
( 2 ) Further, the galvanometer being a sensitive instrument, a large current can damage its coil.
To overcome these problems, a high value resistance called series resistance is connected in series with the galvanometer. If G is the resistance of the modified galvanometer, the new equivalent resistance of the circuit will be R' = R + ( RG / G) which is the same as the equivalent resistance of the original circuit. Thus, resistance of the circuit is not changed much and as the value of G is large, most of the current flows through R which helps to measure correct value of IR. Moreover, very small current flows through the galvanometer due to its large resistance and is thus protected.
( b ) Ammeter: -
Ammeter is used for measuring current. Galvanometer is a current sensing device which is used for this purpose. However, there are two practical difficulties in using galvanometer as an ammeter:
( 1 ) If we want to measure the current flowing through the resistor R, the current measuring instrument is to be connected in series with it. This adds resistance G of the instrument in the circuit thereby altering the current in the resistor from the original value I to I’.
( 2 ) Further, a moving coil galvanometer is very sensitive and even a small current through it gives full scale deflection. Also the heat ( I2Gt ) produced in it due to large current can damage its coil.
To overcome these problems, a low value resistance called shunt is connected in parallel to the galvanometer. As its value is much smaller than G, most of the current flows through it and the galvanometer does not get damaged. Moreover, the equivalent resistance of the modified galvanometer is lower than that of the shunt which when connected in the circuit does not alter its resistance appreciably and hence the true value of the current is measured.
( c ) Wheatstone Bridge : -
The network shown in the figure is known as Wheatstone bridge. It is a closed loop made up of four resistors P, Q, R and S. A source of emf ( battery ) is connected across AC and a galvanometer is connected across BD. Three of the four resistors are known whose values are so adjusted that the galvanometer shows zero deflection. In this condition, Wheatstone bridge is said to be balanced.
Applying Kirchhoff’s second rule to the loop A - B - D - A under the balanced condition,
- P I 1 + R I 2 = 0 ∴ P I 1 = R I 2 ... ... ( 1 )
Similarly, applying Kirchhoff’s second rule to the loop B - C - D - B,
- Q I 1 + S I 2 = 0 ∴ Q I 1 = S I 2 ... ... ( 2 )
Dividing equation ( 1 ) by equation ( 2 ), we have
P / Q = R /S
Hence by using the values of the three known resistors in the above equation, the value of the fourth unknown resistor can be calculated.
The circuit constructed as shown in the adjoining figure is used in the laboratory to find the value of unknown resistance using Wheatstone bridge principle.
Here, a constantan resistive wire of uniform diameter is used in place of resistors R and S. The wire is mounted on a wooden plank alongwith a meter rule. Copper strips are connected at the ends A and B
of the wire as shown in the figure. The terminals on this strip are connected to a battery. Another copper strip is fixed between these two strips forming two gaps. In one gap, an unknown resistor P is connected and in the other a known resistor Q is connected. One end of a galvanometer is connected to the mid-point D of this strip and the other end to a jockey which can slide on the wire AB. For a given value Q, the jockey is slided on the wire in such a way that galvanometer shows zero deflection.
( d ) Potentiometer: -
When we try to measure emf of the battery using a voltmeter, some current does flow through the battery. Hence, voltmeter measures terminal voltage V and not the emf e. If the term I r in the above equation is zero, then only the voltmeter can measure emf of the battery. As internal resistance of the battery is not zero, this means that the current I must be zero. This is not possible in a voltmeter. Hence voltmeter cannot measure emf of the battery. To measure emf of the battery, a device known as potentiometer is used.
Principle of potentiometer: -
Potentiometer is such an arrangement in which one can obtain a continuously varying p.d., the principle of which can be utilized to measure emf of a battery with a suitable circuit. A battery having emf e and internal resistance r is connected in series with a resistance box R and a long resistive wire of uniform diameter ( so that its resistance per unit length is constant ).
The potential difference between any two points of the potentiometric wire is directly proportional to the length of the wire between the two points. Points A and C behave like the positive and negative poles of a battery. By changing the position of C, one can obtain the continuously varying emf.
Voltmeter is used to measure the potential difference between any two points of a circuit.
Galvanometer with suitable modification is used for this purpose. However, there are two practical difficulties in using galvanometer as a voltmeter:
( 1 ) To measure potential difference across a circuit element, galvanometer has to be connected in parallel to it. This alters the resistance of the circuit and the current flowing through the circuit element and hence the potential difference across it.
( 2 ) Further, the galvanometer being a sensitive instrument, a large current can damage its coil.
To overcome these problems, a high value resistance called series resistance is connected in series with the galvanometer. If G is the resistance of the modified galvanometer, the new equivalent resistance of the circuit will be R' = R + ( RG / G) which is the same as the equivalent resistance of the original circuit. Thus, resistance of the circuit is not changed much and as the value of G is large, most of the current flows through R which helps to measure correct value of IR. Moreover, very small current flows through the galvanometer due to its large resistance and is thus protected.
( b ) Ammeter: -
Ammeter is used for measuring current. Galvanometer is a current sensing device which is used for this purpose. However, there are two practical difficulties in using galvanometer as an ammeter:
( 1 ) If we want to measure the current flowing through the resistor R, the current measuring instrument is to be connected in series with it. This adds resistance G of the instrument in the circuit thereby altering the current in the resistor from the original value I to I’.
( 2 ) Further, a moving coil galvanometer is very sensitive and even a small current through it gives full scale deflection. Also the heat ( I2Gt ) produced in it due to large current can damage its coil.
To overcome these problems, a low value resistance called shunt is connected in parallel to the galvanometer. As its value is much smaller than G, most of the current flows through it and the galvanometer does not get damaged. Moreover, the equivalent resistance of the modified galvanometer is lower than that of the shunt which when connected in the circuit does not alter its resistance appreciably and hence the true value of the current is measured.
( c ) Wheatstone Bridge : -
The network shown in the figure is known as Wheatstone bridge. It is a closed loop made up of four resistors P, Q, R and S. A source of emf ( battery ) is connected across AC and a galvanometer is connected across BD. Three of the four resistors are known whose values are so adjusted that the galvanometer shows zero deflection. In this condition, Wheatstone bridge is said to be balanced.
Applying Kirchhoff’s second rule to the loop A - B - D - A under the balanced condition,
- P I 1 + R I 2 = 0 ∴ P I 1 = R I 2 ... ... ( 1 )
Similarly, applying Kirchhoff’s second rule to the loop B - C - D - B,
- Q I 1 + S I 2 = 0 ∴ Q I 1 = S I 2 ... ... ( 2 )
Dividing equation ( 1 ) by equation ( 2 ), we have
P / Q = R /S
Hence by using the values of the three known resistors in the above equation, the value of the fourth unknown resistor can be calculated.
The circuit constructed as shown in the adjoining figure is used in the laboratory to find the value of unknown resistance using Wheatstone bridge principle.
Here, a constantan resistive wire of uniform diameter is used in place of resistors R and S. The wire is mounted on a wooden plank alongwith a meter rule. Copper strips are connected at the ends A and B
of the wire as shown in the figure. The terminals on this strip are connected to a battery. Another copper strip is fixed between these two strips forming two gaps. In one gap, an unknown resistor P is connected and in the other a known resistor Q is connected. One end of a galvanometer is connected to the mid-point D of this strip and the other end to a jockey which can slide on the wire AB. For a given value Q, the jockey is slided on the wire in such a way that galvanometer shows zero deflection.
( d ) Potentiometer: -
When we try to measure emf of the battery using a voltmeter, some current does flow through the battery. Hence, voltmeter measures terminal voltage V and not the emf e. If the term I r in the above equation is zero, then only the voltmeter can measure emf of the battery. As internal resistance of the battery is not zero, this means that the current I must be zero. This is not possible in a voltmeter. Hence voltmeter cannot measure emf of the battery. To measure emf of the battery, a device known as potentiometer is used.
Principle of potentiometer: -
Potentiometer is such an arrangement in which one can obtain a continuously varying p.d., the principle of which can be utilized to measure emf of a battery with a suitable circuit. A battery having emf e and internal resistance r is connected in series with a resistance box R and a long resistive wire of uniform diameter ( so that its resistance per unit length is constant ).
The potential difference between any two points of the potentiometric wire is directly proportional to the length of the wire between the two points. Points A and C behave like the positive and negative poles of a battery. By changing the position of C, one can obtain the continuously varying emf.
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