Finding the maximum value of current

In summary, a galvanometer with 50 divisions on the scale and a current sensitivity of 0.1 m A/division has a resistance of 40Ω. When a shunt resistance of 0.1 Ω is added, the maximum value of the current that can be measured is 2 A. This is found by using the formula for current sensitivity and understanding the relationship between the current and voltage in the circuit.
  • #1
Muthumanimaran
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2

Homework Statement


galvanometer with 50 divisions on the scale requires a current sensitivity of 0.1 m A/division. The resistance of the galvanometer is 40Ω. If a shunt resistance 0.1 Ω is connected across it, find the maximum value of the current that can be measured using this ammeter.

Homework Equations


current sensitivity = $\frac{\theta}{I}$
where $\theta$ is the division and $I$ is the current

$\frac{I_{g}}{I-{I_{g}}}G=S$
$I_{g}$ is the current through the galvanometer. $I$ is the total current. $G$ is galvanometer resistance and $S$ is the shunt resistance.

The Attempt at a Solution



using the first expression, I found the current through the circuit, i.e,
$$I=\frac{50}{0.1mA}$$
or

$$I=5\times10^{5}$$

next I substituted in the above formula, I get $I_{g}$ is equal to 1247 A. But it is not the correct answer. The correct answer is 2 A. Definitely I made a mistake, I understand the mistake is purely conceptual. I believe the maximum current that can be measured is not $I_{g}$, so help me to understand the problem.
 
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  • #2
What is current is passing through the meter without the shunt at full scale?
 
  • #3
The reason I ask is because if full scale is 50 divisions and there is .1ma (100 microamps) per division then the meter will draw 5 ma at full scale. Knowing this in conjunction with the 40 ohm series resistance of the meter means it has a voltage of 40 x 5 ma or .2 volts. Now the .1 ohm is in parallel with the 40 ohm series meter resistance. At this point the current through the .1 ohm resistance can be found and from that the maximum current that will drive the meter to full scale. Let me know if you still need help
 
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  • #4
Muthumanimaran said:
current sensitivity of 0.1 m A/division.
...
current sensitivity = ##\frac{\theta}{I}## where ##\theta## is the division and ##I## is the current
Do you not see a conflict between those two statements?

In this forum, the latex requires either a double dollar sign (giving it a line to itself) or a double hash sign (#) to embed it within a line:
Muthumanimaran said:
##\frac{I_{g}}{I-{I_{g}}}G=S##
##I_{g}## is the current through the galvanometer. ##I## is the total current. ##G## is galvanometer resistance and ##S## is the shunt resistance.
 
  • #5
Inventive said:
The reason I ask is because if full scale is 50 divisions and there is .1ma (100 microamps) per division then the meter will draw 5 ma at full scale. Knowing this in conjunction with the 40 ohm series resistance of the meter means it has a voltage of 40 x 5 ma or .2 volts. Now the .1 ohm is in parallel with the 40 ohm series meter resistance. At this point the current through the .1 ohm resistance can be found and from that the maximum current that will drive the meter to full scale. Let me know if you still need help
Thanks for your help. I understood the mistake and got the correct solution.
 
  • #6
Your welcome
 

Related to Finding the maximum value of current

1. What is the maximum value of current?

The maximum value of current is the highest amount of electric current that can flow through a circuit or material without causing damage or exceeding its capacity. It is typically measured in amperes (A) and can vary depending on the specific circuit or material.

2. How is the maximum value of current determined?

The maximum value of current is determined by the properties of the circuit or material, such as its resistance and voltage. These factors can be used to calculate the maximum current that can flow through the circuit without causing damage.

3. Why is it important to find the maximum value of current?

It is important to find the maximum value of current in order to ensure the safe and efficient operation of a circuit or material. Knowing the maximum current can help prevent electrical fires, damage to equipment, and other hazards.

4. What factors can affect the maximum value of current?

The maximum value of current can be affected by a variety of factors, including the type and quality of the conductive material, the temperature, and the length and thickness of the circuit. Changes in these factors can alter the resistance and capacity of the circuit, ultimately affecting the maximum current.

5. How can the maximum value of current be increased?

The maximum value of current can be increased by using materials with lower resistance, increasing the voltage in the circuit, and adjusting the length and thickness of the circuit. However, it is important to note that increasing the maximum current beyond the recommended limit can be dangerous and should be done with caution.

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