Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A galvanometer having 30 divisions has current sensitivity of 20 µA/div. It has a resistance of 25 ohm. How will you convert it to an ammeter measuring upto 1 ampere? How will you now convert this ammeter into a voltmeter reading upto 1 volt?
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: To convert the galvanometer into an ammeter, we need to calculate the shunt resistance required to bypass a portion of the current.
The galvanometer has a current sensitivity of 20 µA/div and 30 divisions, so the full-scale deflection (FSD) current, $I_g$, is given by:
$$I_g = 30 imes 20 imes 10^{-6} A = 0.0006 A = 0.6 mA$$
For the ammeter to read up to 1 A, we will need to pass 1 A through the ammeter.
Step 2: The shunt current ($I_s$) that would bypass the galvanometer can be calculated as:
$$I_s = I - I_g = 1 A - 0.0006 A = 0.9994 A$$
Step 3: We can now use the shunt resistance formula:
$$R_s = rac{V_g}{I_s}$$
where $V_g$ is the voltage across the galvanometer. The voltage across the galvanometer can be calculated using Ohm's law:
$$V_g = I_g imes R_g = 0.0006 A imes 25 ext{ ohm} = 0.015 V$$
Now substituting the values:
$$R_s = rac{0.015 V}{0.9994 A} \approx 0.01501 ext{ ohm}$$
This is the shunt resistance required to convert the galvanometer into an ammeter measuring up to 1 A.
Step 4: To convert the ammeter into a voltmeter reading up to 1 V, we will need to connect a series resistance ($R_v$) to the ammeter. The total voltage across the ammeter when it shows full-scale deflection has to be set to 1 V. Using Ohm's law:
$$V = I imes R$$
The maximum current through the circuit when the ammeter is measuring full scale is still 1 A:
$$1V = 1A imes (R_g + R_v)$$
We already have $R_g = 25 ext{ ohm}$, thus:
$$R_v = rac{1V}{1A} - R_g = 1 - 25 = -24 ext{ ohm}$$
Since negative resistance is not possible, we cannot convert this ammeter to voltmeter accurately up to 1 V with this setup. Thus, the procedure for conversion to ammeter is successful but the voltmeter conversion is not possible with the provided galvanometer.
Therefore, to summarize, the ammeter can be achieved with shunt resistance approximately 0.015 ohm, but the conversion to the voltmeter to read 1 V is not feasible.
The galvanometer has a current sensitivity of 20 µA/div and 30 divisions, so the full-scale deflection (FSD) current, $I_g$, is given by:
$$I_g = 30 imes 20 imes 10^{-6} A = 0.0006 A = 0.6 mA$$
For the ammeter to read up to 1 A, we will need to pass 1 A through the ammeter.
Step 2: The shunt current ($I_s$) that would bypass the galvanometer can be calculated as:
$$I_s = I - I_g = 1 A - 0.0006 A = 0.9994 A$$
Step 3: We can now use the shunt resistance formula:
$$R_s = rac{V_g}{I_s}$$
where $V_g$ is the voltage across the galvanometer. The voltage across the galvanometer can be calculated using Ohm's law:
$$V_g = I_g imes R_g = 0.0006 A imes 25 ext{ ohm} = 0.015 V$$
Now substituting the values:
$$R_s = rac{0.015 V}{0.9994 A} \approx 0.01501 ext{ ohm}$$
This is the shunt resistance required to convert the galvanometer into an ammeter measuring up to 1 A.
Step 4: To convert the ammeter into a voltmeter reading up to 1 V, we will need to connect a series resistance ($R_v$) to the ammeter. The total voltage across the ammeter when it shows full-scale deflection has to be set to 1 V. Using Ohm's law:
$$V = I imes R$$
The maximum current through the circuit when the ammeter is measuring full scale is still 1 A:
$$1V = 1A imes (R_g + R_v)$$
We already have $R_g = 25 ext{ ohm}$, thus:
$$R_v = rac{1V}{1A} - R_g = 1 - 25 = -24 ext{ ohm}$$
Since negative resistance is not possible, we cannot convert this ammeter to voltmeter accurately up to 1 V with this setup. Thus, the procedure for conversion to ammeter is successful but the voltmeter conversion is not possible with the provided galvanometer.
Therefore, to summarize, the ammeter can be achieved with shunt resistance approximately 0.015 ohm, but the conversion to the voltmeter to read 1 V is not feasible.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistanc…
The series combination of two batteries, both of the same emf 10V, but different internal resistanc…
Four resistances of 15 Ω Ω , 12 Ω Ω , 4 Ω Ω and 10 Ω Ω respectively in cyclic order to form Wheatst…
Match the following:
The following table gives the lengths of four copper rods at the same temperat…
Match the statements in Column I with the current element in Column II
Column - IColumn - II(A)Curr…
A continuous beam of electrons emitted by a heating filament are accelerated in free space by an el…