A galvanometer having coil resistance 10 Ω shows a full scale deflection for a current of 3 mA. For it to measure a current of 8 A, the value of the shunt should be:
A galvanometer having coil resistance 10 Ω shows a full scale deflection for a current of 3 mA. For it to measure a current of 8 A, the value of the shunt should be:
- \(10^{- 3}\; Ω\)
- \(7.5 \times 10^{- 3}\; Ω\)
- \(6.75 \times 10^{- 3}\; Ω\)
- \(3.75 \times 10^{- 3}\; Ω\)
The Correct Option is D
Approach Solution - 1
To solve this problem, we need to determine the value of the shunt resistor (\(R_s\)) that allows the galvanometer to measure a current of 8 A when the full-scale deflection current is only 3 mA. This involves understanding the concept of shunt resistance in parallel with a galvanometer.
The galvanometer shows a full-scale deflection at a current denoted as \(I_g\), which is given as 3 mA or \(3 \times 10^{-3} \, \text{A}\). The total current \(I\) that needs to be measured is 8 A.
The shunt resistance (\(R_s\)) is used to bypass the majority of the current such that only a small portion passes through the galvanometer. The current through the shunt is given by \(I_s = I - I_g\).
The relation between the galvanometer, shunt resistance, and the total current is given by:
\(V_g = I_g \cdot R_g = I_s \cdot R_s\)
Where:
- \(V_g\) is the voltage across the galvanometer and the shunt (both in parallel)
- \(R_g\) is the resistance of the galvanometer coil, given as 10 Ω
- \(I_s = I - I_g = 8 - 0.003 = 7.997\) A
Using the above relation:
\(I_g \cdot R_g = I_s \cdot R_s\)
Substituting the values:
\(3 \times 10^{-3} \times 10 = 7.997 \times R_s\)
Simplifying gives:
\(0.03 = 7.997 \times R_s\)
Thus, the shunt resistance is:
\(R_s = \frac{0.03}{7.997} \approx 3.75 \times 10^{-3} \, \Omega\)
Therefore, the value of the shunt resistance required to measure a current of 8 A is \(3.75 \times 10^{-3} \, \Omega\), which corresponds to the correct option.
Approach Solution -2
Step 1: Given Data: - Galvanometer resistance \( G = 10 \Omega \) - Full-scale deflection current \( I_g = 3 \, \text{mA} = 3 \times 10^{-3} \, \text{A} \) - Desired current to be measured \( I = 8 \, \text{A} \)
Step 2: Calculate the Shunt Resistance \( S \): - In order to convert the galvanometer into an ammeter, the shunt resistance \( S \) is given by:
\[ S = \frac{I_g \, G}{I - I_g} \]
Step 3: Substitute the Values:
\[ S = \frac{(3 \times 10^{-3}) \times 10}{8 - 0.003} \\ S = \frac{0.03}{7.997} \approx 3.75 \times 10^{-3} \, \Omega \]
So, the correct answer is : \( 3.75 \times 10^{-3} \, \Omega \)
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Concepts Used:
Resistance
Resistance is the measure of opposition applied by any object to the flow of electric current. A resistor is an electronic constituent that is used in the circuit with the purpose of offering that specific amount of resistance.
R=V/I
In this case,
v = Voltage across its ends
I = Current flowing through it
All materials resist current flow to some degree. They fall into one of two broad categories:
- Conductors: Materials that offer very little resistance where electrons can move easily. Examples: silver, copper, gold and aluminum.
- Insulators: Materials that present high resistance and restrict the flow of electrons. Examples: Rubber, paper, glass, wood and plastic.
Resistance measurements are normally taken to indicate the condition of a component or a circuit.
- The higher the resistance, the lower the current flow. If abnormally high, one possible cause (among many) could be damaged conductors due to burning or corrosion. All conductors give off some degree of heat, so overheating is an issue often associated with resistance.
- The lower the resistance, the higher the current flow. Possible causes: insulators damaged by moisture or overheating.