Question

The full scale deflection current of an ammeter is 1mA and its internal resistance is $100\Omega$. If this meter is to have full deflection of 5A, what is the value of the shunt resistance to be used?

• A. $49.99\Omega$
• B. $1/49.99\Omega$
• C. $1\Omega$
• D. $2\Omega$

Hint:

To quickly calculate ammeter shunts, remember that the shunt resistance must always be much smaller than the meter resistance.
Using the relation \( I_m R_m = I_{sh} R_{sh} \) directly can also prevent algebraic mistakes.
Since the current division is extremely high, the shunt resistance is approximately \( \frac{R_m}{m} \).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question requires us to determine the value of the shunt resistance ($R_{sh}$) needed to extend the range of an ammeter.

Step 2: Key Formula or Approach:
The shunt resistance required to extend the range of an ammeter is given by the formula:
\[ R_{sh} = \frac{R_m}{m - 1} \] where:
\( R_m \) is the internal resistance of the meter.
\( m \) is the multiplying factor, defined as \( m = \frac{I}{I_m} \).
\( I \) is the new full-scale deflection current.
\( I_m \) is the original full-scale deflection current of the meter.

Step 3: Detailed Explanation:

• Identify the given parameters from the problem:
Original full-scale current, \( I_m = 1\text{ mA} = 1 \times 10^{-3}\text{ A} \).
Internal resistance of the meter, \( R_m = 100\ \Omega \).
New desired full-scale deflection current, \( I = 5\text{ A} \).

• Calculate the multiplying factor \( m \):
\[ m = \frac{I}{I_m} = \frac{5}{1 \times 10^{-3}} = 5000 \]
• Substitute the value of \( m \) and \( R_m \) into the shunt resistance formula:
\[ R_{sh} = \frac{100}{5000 - 1} = \frac{100}{4999}\ \Omega \]
• Simplify the expression to match the options:
\[ R_{sh} = \frac{1}{49.99}\ \Omega \]
• This small shunt resistance is connected in parallel with the meter so that the bulk of the current (4.999 A out of 5 A) flows through the shunt, protecting the sensitive meter coil.