Calibration of Voltmeter:
Observations measured from voltmeter is errorful due to different reasons:
(i) In built mechanical error, (ii) Parallex error,
(iii) Unsymmetricity in the spring of voltmeter etc. Potentiometer can increase precise value of potential difference.
Checking the errors of observations of voltmeter by potentiometer is known as Calibration of Voltmeter.
In figure necessary circuit diagram is shown for calibration of voltmeter. Primary circuit is usually connected as section before.
In secondary circuit positive terminal of standard cell is connected at point A (high potential end) while negative terminal is connected with the terminal 1 of two way key. In this circuit other cell ε, rheostat Rh2, key K2 and resistance box (R.B.) is connected in series as shown in figure. The high potential end of R.B. is connected at A while lower potential end is connected at the terminal 3 of two way key. The voltmeter which is to be calibrated should be connected across the ends of R.B. The middle terminal of two way key is connected with the one end of galvanometer (G) and other end of (G) is connected with jockey.
Working: Firstly we completed the primary circuit and insert the plug between terminal 1 and 2 and by the help of jockey finding balancing length l0 for the standard cell εs
\(\varepsilon_{s}=k l_{0} \quad \text { or } \quad k=\frac{\varepsilon_{s}}{l_{0}}\) …………….. (1)
k is potential gradient.
By the standardisation of cell, then find out k.
Now eliminate the plug between 1 and 2 and insert it between 2 and 3. Now key K2 be closed and suitable resistance out from R.B. By the help of Rh2 necessary current pass through the resistance and takes the deflection in voltmeter, which is V. It is errorful observation, corresponding to V. Find out the real value of potential difference by potentiometer. Find the balancing length l2. Now by the principle of potentiometer the real value of potential difference
V’ = kl2
V’ = \(\left(\frac{\varepsilon_{s}}{l_{0}}\right)\)l2 ………… (2)
Error in the observation of voltmeter
ΔV = V – V’
By the help of R.B. and Rh2, observe different values of voltmeter and for it find corresponding values of potential difference by potentiometer. Now taking difference of V (observations of voltmeter) and V’ (potential difference by potentiometer) we can find error in it
ΔV = V – V’
Calibration Curve: A graph is plotted between the readings of voltmeter and the corresponding errors. This graph is called calibration curve of the voltmeter. The graph has been no definite shape. The any graph of calibration is shown in figure.
Calibration of Ammeter:
Checking of the errors of observations of electric current by ammeter by potentiometer is known as calibration of ammeter.
Circuit: For calibration of ammeter necessary circuit diagram is shown in figure
Primary circuit is usually connected. In secondary circuit positive terminal of standard cell εs is connected at point A (high potential end) while negative terminal is connected with the terminal 1 of two-way key. In this circuit other cell ε1 rheostat Rh2, key K2 and 1 Ω coil and ammeter are connected in series as shown in figure.
Working: Firstly we complete the primary circuit and insert the plug between terminal 1 and 2 and by the help of jockey find balancing length l0 for the standard cell εs
εs = kl0
or k = \(\frac{\varepsilon_{s}}{l_{0}}\) ………………… (1)
k is potential gradient. By the standardisation of cell find out the k. Now eliminating the plug between the terminals 1 and 2 and inserting it between 2 and 3. Now key K2 is closed. By the help of Rh2 necessary current pass through the 1 Ω coil and takes the deflection in ammeter, which is I. It is errorful observation.
By Ohm’s law, current flowing through 1 Ω resistance is equal to the potential difference across the ends of the 1 Ω coil. Obtain balancing length l2 for the potential difference across the ends of the 1 Ω coil. Obtain balancing length l2 for the potential difference V’ which is across the ends of the coil.
V’ = kl2 but V’ = I’R, R = 1 Ω
I’ = kl2
I’ = \(\left(\frac{\varepsilon_{s}}{l_{0}}\right)\) l2 …(2)
I’ is the real value of current which is measured by the potentiometer. Now obtain the error in current observed by ammeter as ΔI.
ΔI = I – I’
For different readings of ammeter obtain corresponding real current by potentiometer then the corresponding error will be I – I’. Plotting the curve between I – I’ and I which is called calibrated curve of ammeter. Zig-zag curve is obtained as shown in figure
We can find real reading by calibrated curve
