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Chapter 27: Problem 87

Mark correct option or options: (a) The current sensitivity of a galvanometer is defined as the deflection in milimeters produced on a scale placed at a distance of one metre from the galvanometer mirror, when a current of \(10^{-6}\) A passes through galvanometer coil (b) Current sensitivity \(=\mathrm{NAB/C}\) (c) Charge sensitivity \(=\frac{2 \pi}{T} \times\) current sensitivity (d) all the above

Short Answer

Expert verified
Statements (b) and (c) are correct.

Step by step solution

01

Explain the Problem

The problem provides four statements related to the definitions of sensitivity in galvanometers and asks us to determine the correct definition or definitions about galvanometer sensitivity, current sensitivity, and charge sensitivity.
02

Analyze Statement (a)

Statement (a) describes the current sensitivity of a galvanometer in terms of a physical setup involving deflection on a scale one meter away. This is not the standard definition of current sensitivity which is typically in terms of angle per unit current.
03

Verify Statement (b)

Statement (b) provides a formula for current sensitivity: Current sensitivity \( = \frac{NAB}{C} \), where \( N \) is the number of turns, \( A \) is the area, \( B \) is the magnetic field strength, and \( C \) is the torsional constant. This is indeed a correct formula for current sensitivity.
04

Evaluate Statement (c)

Statement (c) relates charge sensitivity to current sensitivity with a formula: Charge sensitivity \( = \frac{2 \pi}{T} \times \text{current sensitivity} \). This formula relates the two sensitivities utilizing the oscillation period \( T \), aligning with typical definitions involving time and charge.
05

Conclusion for Statement (d)

Statement (d) asserts that all previous statements are correct, which our analysis shows is not the case because statement (a) is incorrect.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Current Sensitivity Formula
Understanding the current sensitivity of a galvanometer is important for accurately measuring small currents. Current sensitivity essentially describes how responsive the galvanometer is to a tiny amount of current. In formulaic terms, current sensitivity is defined as \( \frac{NAB}{C} \). Here:
  • \( N \) represents the number of turns in the coil.
  • \( A \) is the area of the coil.
  • \( B \) stands for the magnetic field strength.
  • \( C \) is the torsional constant of the coil.
This formula shows that the current sensitivity increases with more coil turns, larger coil area, or stronger magnetic field. Conversely, a higher torsional constant will reduce sensitivity. It鈥檚 important to note that sensitivity is reflected in the deflection angle produced by the galvanometer for a given current.
Charge Sensitivity Definition
Charge sensitivity offers another lens to view a galvanometer's effectiveness. Specifically, it measures how much the galvanometer needle moves per unit charge passing through. To determine the relationship between charge and current sensitivity, consider the formula: Charge sensitivity \( = \frac{2 \pi}{T} \times \text{current sensitivity} \).
  • \( T \) represents the oscillation period of the current in the circuit.
This definition indicates that charge sensitivity is directly proportional to current sensitivity, adjusted for the oscillation period. Essentially, it shows that the faster the oscillation of current, relative to its period, the more sensitive the device is to charge.
Galvanometer Function
A galvanometer is an essential instrument in physics and engineering, primarily used to detect and measure small electrical currents. It operates on the principle that a magnetic field is created when current flows through a coil, inducing a mechanical movement within the galvanometer.
  • Inside the device, a needle is attached to a coil that is suspended in a magnetic field.
  • When current passes through this coil, it experiences a torque due to the magnetic field, causing the needle to deflect.
The angle of deflection is proportional to the current running through the coil, meaning the galvanometer serves as a direct indicator of current strength. Its design ensures that even tiny amounts of current can be detected, making it a sensitive and precise tool for electrical measurements.

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Most popular questions from this chapter

A particle of mass \(m\), carrying a charge \(q\) is lying at the origin in a uniform magnetic field directed along \(x\) -axis. At the instant \(t=0\) it is given a velocity \(v_{0}\) at an angle \(\theta\) with the \(y\) -axis, in the \(x-y\) plane. The coordinates of the particle after one revolution will be : (a) \(\left(0,0 \cdot \frac{2 \pi m v_{0} \sin \theta}{q B}\right)\) (b) \(\left(\frac{2 \pi m v_{0} \sin \theta}{q B} \cdot 0,0\right)\) (c) \(\left(\frac{2 \pi m v_{0} \sin \theta}{a B} 0,4\right)\) (d) \((0,0,0)\)

The restoring couple in the moving coil galvanometer is because of : (a) magnetic field (b) material of the coil (c) twist produced in the suspension (d) current in the coil

An insulating rod of length \(l\) carries a charge \(q\) distributed uniformly on it. The rod is pivoted at an end and is rotated at a frequency \(f\) about a fixed perpendicular axis. The magnetic moment of the system is : (a) zero (b) \(\pi q f l^{2}\) (c) \(\frac{1}{2} \pi q f l^{2}\) (d) \(\frac{1}{3} \pi q f l^{2}\)

A conducting loop carrying a current is placed in a non-uniform magnetic field perpendicular to the plane of loop. Then : (a) loop must experience force (b) loop may experience torque (c) loop must experience torque (d) none of the above

A point charge \(q\) is placed near a long straight wire carrying current \(I\), then : (a) there is small charge density on the surface of wire (b) there is no charge density on the surface of wire (c) no force is exerted by wire on the point charge \(q\) (d) a large force is exerted by wire on the point charge \(q\)
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