The Moving Coil Galvanometer MCQ Quiz - Objective Question with Answer for The Moving Coil Galvanometer - Download Free PDF

Calculation:

The magnetic torque on the coil is balanced by the restoring torque. The torque due to current is given by:

Deflection torque = number of turns × area × magnetic field × current = nABi

Restoring torque = torsional constant × angle = kθ

Equating the torques:

i = (kθ) / (nAB)

Substitute the given values:

i = (10⁻⁴ × 0.2) / (50 × 2 × 10⁻⁴ × 0.02) = 0.1 A

This is the maximum current the galvanometer can measure without damage (ig).

To measure up to 1 A, a shunt resistor (S) must be added in parallel. Using Kirchhoff's law:

igG = (i - ig)S

S = igG / (i - ig)

Substituting values:

S = (0.1 × 50) / (1 - 0.1) = 5 / 0.9 = 5.55 Ω

Answer: 5.55 Ω

Calculation:

Let R be the resistance of the ammeter & I be the maximum current passing through the ammeter.

In the first case \(0.03\; \text{A}\) is main current and in the second case \(0.06\; \text{A}\) is main current.

\(I=\frac{0.03 \times 4r}{(R+4r)}\) for Ist case

\(I=\frac{0.06 \times r}{(R+r)}\) for second case

\(\frac{0.03 \times 4r}{R+4r}=\frac{0.06 \times r}{(R+r)}\)

\(R+4r=2R+2r \Rightarrow R=2r\)

The value of

\(I=\frac{0.03 \times 4r}{2r+4r}=\frac{0.03 \times 4r}{6r}\)

\(=0.02\; \text{A}\)

This is the maximum value of current in the ammeter.

Explanation:

A galvanometer can be converted into a voltmeter by connecting a high resistance in series with its coil. This is because a voltmeter is used to measure the potential difference across two points in a circuit and it must draw a very small current to avoid altering the circuit conditions. By placing a high resistance in series with the galvanometer, the overall resistance is increased, ensuring that only a small current passes through the galvanometer, thus preventing it from affecting the circuit.

Option 1, which suggests a high resistance in parallel, would not be suitable because it would allow more current to pass through the galvanometer, potentially damaging it and affecting the circuit conditions. Option 3 and Option 4, which suggest low resistance, would also not be appropriate because they would not limit the current sufficiently.

∴ The correct answer is option 2: High resistance in series with its coil.

 The correct answer is Option 4: Low resistance wire in parallel.

Explanation:

Galvanometer: Sensitive instrument to detect small electric currents.

Shunt Resistance: Low resistance connected in parallel to galvanometer to protect it from damage due to high currents.

Purpose: It allows most of the current to bypass the galvanometer, limiting the current through the galvanometer coil and thus protecting it.

A low resistance wire connected in parallel (called a shunt) diverts excess current, thereby safeguarding the galvanometer.

This prevents damage by reducing the amount of current passing through the galvanometer coil. 

Calculation:

(A) τ = Cθ ⇒ [ML²T^–2] = [C][1]

(B) C.S = \(\frac{\theta}{\mathrm{I}}=\frac{\mathrm{BNA}}{\mathrm{C}}\);

(C) V.S ∝ \(\frac{\mathrm{NAB}}{\mathrm{CR}}\quad \quad \mathrm{R} \rightarrow \mathrm{NR}\)

(D) False [Theory]

(E) E [False]

 \(\rm \quad \quad C.S \propto N \) ⇒ C.S. = \(\frac{\mathrm{NAB}}{\mathrm{C}}\)

The correct answer is A low resistance in parallel.

Explanation:

We can convert a Galvanometer into an ammeter by connecting a low resistance in parallel.

• Electric current is defined as the rate of flow of charge or electron, so its direction is the flow of positive charge.
• SI unit of the electricity is Ampere(A) and it is a scalar quantity.
• Resistance is the opposition delivered by the conductor in which current flows through it.
• A device that is used to measure electric current in a circuit is called an ammeter. The resistance of an ideal ammeter is always Zero and is always connected in the circuit in series.
• A voltmeter is a device that is used to measure the potential difference between the two points in a circuit. The resistance of an ideal voltmeter is infinite.
• A galvanometer is a device that is used to detect and measure small electric currents in any circuit. It can measure current up to 10-6 Ampere.
• Now the interesting fact is:

We can convert a Galvanometer into an ammeter by connecting a shunt parallel to it.

We can also convert a Galvanometer into a voltmeter by connecting a very high resistance in its series

CONCEPT:

• Moving coil Galvanometer: It is a device that is used to measure and detect the small amount of electric charge i.e. electric current.
  •  It is the most sensitive device and used in many electrical instruments. It is the major basic component of Ammeter and Voltmeter.
• Principle: Moving coil galvanometer is based on the fact that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

EXPLANATION:

• From above it is clear that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

∴ The moment of the deflecting couple (τ) = nBIA

Where

n = number of turns,

B = magnetic field,

I = current

A = area of coil

CONCEPT:

• Galvanometer: The instrument which is used to measure and determine the direction of electric current in a magnetic field is called a Galvanometer.
  • It consists of a coil having an electric current.
• The ratio of change in deflection of a galvanometer to the change in current is called the current sensitivity of the galvanometer.
• The angular deflection per unit voltage applied is called a voltage sensitivity of the galvanometer.

The sensitivity of Galvanometer is given by:

Current sensitivity of galvanometer (Si) = dθ/di = NBA/K

Voltage sensitivity (S_V) = S_i/R

Where N is a number of turns, B is the magnetic field, A is the area of the coil and K is constant, dθ is change in deflection and dI is change in current and R is resistance.

CALCULATION:

Given that:

Current sensitivity (S_i) = 5 div/ (m A) = 5 × 10³ div/A

Voltage sensitivity (S_V) = 20 div/V

Since Voltage sensitivity (S_V) = S_i/R

Resistance (R) = S_I/ S_V = (5 × 10³ div/A)/ (20 div/V) = 250 Ω

So option 3 is correct.

Concept:

• Moving coil Galvanometer: It is a device that is used to measure and detect the small amount of electric charge i.e. electric current.
  •  It is the most sensitive device and used in many electrical instruments. It is the major basic component of Ammeter and Voltmeter.
• Principle: Moving coil galvanometer is based on the fact that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

Explanation:

• From above it is clear that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

∴ The moment of the deflecting couple (τ) = nBIA

Where n = number of turns, B = magnetic field, I = current and A = area of coil

• When the coil deflects, the suspension wire is twisted. On account of elasticity, a restoring couple is set up in the wire. This couple is proportional to the twist.
• If θ = the angular twist, then,
• The moment of the restoring couple = Cθ 

Where C = restoring couple per unit twist.

At equilibrium,

⇒ Deflecting couple = Restoring couple

Hence we can write,

⇒ nBIA = Cθ

\( \Rightarrow \theta =(\frac{nBA}{C})I\)

Here, n, B, and A are constant

• Therefore, the deflection produced in the moving coil galvanometer is directly proportional to the amount of current passing through it.
• Hence the relation between current and deflection is i ∝ θ.

The correct answer is option 2) i.e. increase the accuracy of the galvanometer

CONCEPT:

• Moving coil galvanometer:  It is an electromagnetic instrument to measure electric current.
  • ​The working principle of a moving coil galvanometer - A current-carrying coil when placed in an external magnetic field experiences a torque.
  • A coil of many turns is suspended between the poles and pieces of a magnet.
  • The pole pieces of the magnet are concave in shape to produce a radial magnetic field. 
  • The deflection of the coil due to the torque is the measure of the current in the coil.

EXPLANATION:

• The radial magnetic field is uniform and ensures that the plane of the coil is parallel to the magnetic field in all directions of the coil.
• This helps in providing a uniform torque on the coil. 
• The uniform torque help in the proper deflection of the coil and hence increases the accuracy of the galvanometer.​

Additional Information

• The sensitivity of the galvanometer can be increased by increasing the number of turns of the coil, using strong magnets or increasing the area of the coil.
•  The magnetic field strength inside a galvanometer is increased by placing a soft iron core inside.

The correct answer is option 3) i.e. putting in parallel resistance of 15 Ω.

CONCEPT:

• Galvanometer: A galvanometer is an instrument used for detecting and indicating the presence of an electric current.
  • ​A galvanometer is a sensitive device and can detect only a very small current of the order of 100 mA.
  • Full-scale deflection of galvanometer refers to the maximum reading available on the meter. Anything beyond this scale cannot be measured by this instrument.
• Conversion of galvanometer into an ammeter: 
  • For measuring a current greater than of the order of 100 mA, a low resistance called a shunt is connected in parallel across the galvanometer.

​

• Let I be the total current in the circuit which is the actual value of current, then the current (I - I_g) passes through a shunt (S), where Ig is current for full-scale deflection of the galvanometer.
• Since G and S are parallel to each other, therefore the potential difference across both is the same.

V_G = V_S

I_gG = (I - I_g)S

⇒ \(S = \frac{I_gG}{(I-I_g)}\)

CALCULATION:

Given that:

The resistance of galvanometer, G = 60 Ω 

Current for full-scale deflection of the galvanometer, I_g = 1 A

The total current in the circuit, I = 5 A

A galvanometer is converted into an ammeter by connecting a shunt in parallel across the galvanometer.

The resistance of shunt connected in parallel, S \(=\frac{I_gG}{(I-I_g)}\)\(= \frac{1 \times 60}{(5-1)}\) = 15 Ω

Concept:

• To convert a galvanometer into an ammeter, a shunt resistor is connected in parallel with the galvanometer.
• A shunt resistor is a low resistance wire or a coil that is connected in parallel with the galvanometer to divert most of the current away from the galvanometer.
• The shunt resistor is designed to have a very low resistance so that most of the current flows through it instead of the galvanometer.
• By connecting the shunt resistor in parallel with the galvanometer, the total current is split between the shunt resistor and the galvanometer.
• The amount of current that flows through the galvanometer is then proportional to the voltage drop across it.
• By selecting an appropriate value for the shunt resistor, the current that flows through the galvanometer can be kept within its range, and the galvanometer can be used as an ammeter to measure higher currents.

The value of the shunt resistor is selected such that the full-scale deflection of the galvanometer occurs when the maximum current to be measured flows through the ammeter. The value of the shunt resistor is calculated using the following formula:

Rs = \(G(\frac{I_g}{I_m} - 1)\)

where:

Rs is the resistance of the shunt resistor
G is the resistance of the galvanometer
I_g is the full-scale deflection current of the galvanometer
I_m is the maximum current to be measured by the ammeter
The shunt resistor should have a very low resistance compared to the resistance of the galvanometer to ensure that most of the current flows through it.

The value of the shunt resistor should also be such that it can handle the maximum current to be measured without getting damaged or changing its resistance value

The correct answer is option (3).

CONCEPT:

• Moving coil Galvanometer: It is a device that is used to measure and detect the small amount of electric charge i.e. electric current.
  •  It is the most sensitive device and used in many electrical instruments. It is the major basic component of Ammeter and Voltmeter.
• Principle: Moving coil galvanometer is based on the fact that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

EXPLANATION:​

• When the coil deflects, the suspension wire is twisted. On account of elasticity, a restoring couple is set up in the wire. This couple is proportional to the twist.
• If θ = the angular twist, then,
• The moment of the restoring couple = Cθ 

Where C = restoring couple per unit twist.

At equilibrium,

⇒ Deflecting couple = Restoring couple

Hence we can write,

⇒ nBIA = Cθ

\( \Rightarrow \theta =(\frac{nBA}{C})I\)

Here, n, B, and A are constant

• Therefore, the deflection produced in the moving coil galvanometer is directly proportional to the amount of current passing through it.
• Hence,  if the current flowing through the moving coil galvanometer is increased, then the deflection in the coil will also increase. 

CONCEPT:

• A galvanometer can be converted into an ammeter by connecting a shunt resistance in parallel to it.
• The shunt resistance should have very low resistance. 
• So, the ammeter (the parallel combination of galvanometer and shunt resistance) will have low resistance.
• To convert a galvanometer into an ammeter of current rating ‘I’, a small resistance ‘S’ (shunt resistance) is connected in parallel across the galvanometer.

\({V_g} = \left( {I - {I_g}} \right)S = {I_g}{R_g}\)

Where Vg is the voltage across the galvanometer, I is the current in the circuit, Ig is the current in the galvanometer, Rg is the resistance of the galvanometer and S is the resistance of the shunt.

CALCULATION:

Given:

Galvanometer coil has resistance Rg = 20 Ω

Full-scale deflection current Ig = 2 mA

Ammeter range I = 6 A

S = IgRg/(I - Ig)

⇒ S = 0.002 × 20/(6 - 0.002)

⇒ S = 6.66 mΩ 

CONCEPT:

• Moving coil Galvanometer: It is a device that is used to measure and detect a small amount of electric charge i.e. electric current.
  •  It is the most sensitive device and used in many electrical instruments. It is the major basic component of the Ammeter and Voltmeter.
• Principle: Moving coil galvanometer is based on the fact that when a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

• Sensitivity: The sensitivity of a galvanometer is higher if the instrument shows a larger deflection for a small value of current

EXPLANATION:

• When a current-carrying rectangular coil is placed in a magnetic field it experiences a torque.

∴ The moment of the deflecting couple (τ) = nBIA

Where n = number of turns, B = magnetic field, I = current and A = area of coil

• When the coil deflects, the suspension wire is twisted. On account of elasticity, a restoring couple is set up in the wire. This couple is proportional to the twist.
• If θ = the angular twist, then,
• The moment of the restoring couple = Cθ 

Where C = restoring couple per unit twist.

At equilibrium,

⇒ Deflecting couple = Restoring couple

Hence we can write,

⇒ nBIA = Cθ

\( \Rightarrow θ =(\frac{nBA}{C})I\)

Here, n, B, and A are constant

• For a given value of electric current (I), the sensitivity of a galvanometer increase when the number of turns, area of the coil, and magnetic field increases whereas the couple per unit twist decreases. Therefore options 1, 2, are 3 are correct.

Additional Information 

Accordingly, it has two types of sensitivity viz.,

1. Current sensitivity
2. Voltage sensitivity

1. Current sensitivity. It is defined as the defection produced in the galvanometer when a unit current flows through it.

If the deflection produced in the galvanometer is θ when current I is passed through it, then,

Current Sensitivity \(\rm S_I=\frac{θ}{I}=\frac{nBA}{k}\)

\(\rm (\because I=\frac{k θ}{nBA})\)

The unit of current sensitivity is rad A^-1 or div A^-1.

2. Voltage Sensitivity. It is defined as the deflection produced in the galvanometer when a unit potential difference is applied across the two terminals of the galvanometer.

If the deflection produced in the galvanometer is θ when a potential difference V is applied across its two terminals then,

Voltage sensitivity, \({S_V} = \frac{θ }{V}\)

If R is the resistance of the galvanometer, then, V = IR.

\(\therefore {S_V} = \frac{θ }{{IR}} = \frac{{nBA}}{{KR}}\)

\((\because I=\frac{Kθ }{nBA})\)

The unit of voltage sensitivity is red V^-1 or div. V^-1.

The current sensitivity of a galvanometer can be increased by;

(i) Increasing the number of turns n in the coil

(ii) Increasing the strength of magnetic field B

(iii) Increasing the area A of the coil

(iv) Decreasing torsion constant k of the spring

The high voltage sensitivity requires the same features as the high current sensitivity, together with low coil resistance (R).