📌 1. Question Description
Moving Coil Galvanometer
A moving coil galvanometer is a sensitive instrument used to detect and
measure small electric currents. It works on the principle that a
current-carrying coil placed in a magnetic field experiences a torque.
τ = NABI sinθ
For a radial magnetic field:
sinθ = 1
Therefore:
τ = NABI
The restoring torque of the suspension is:
τ = kθ
At equilibrium:
NABI = kθ
Therefore:
⭐ I = kθ / NAB
⚙️ 2. Working Principle
The moving coil galvanometer works on the principle that a
current-carrying coil placed in a magnetic field experiences a
magnetic torque.
τ = NABI
The torque rotates the coil. The attached pointer moves over a graduated
scale and the deflection becomes proportional to current.
✔ Deflection θ ∝ Current I
🔧 3. Construction
1. Permanent Magnet
Produces a strong radial magnetic field.
2. Moving Coil
A rectangular coil of many turns of insulated wire.
3. Soft Iron Core
Increases magnetic field strength and helps produce a radial field.
4. Suspension
Provides restoring torque and carries current to the coil.
5. Pointer
Shows the angular deflection on a graduated scale.
6. Damping
Prevents oscillations and allows quick stable readings.
🔬 4. Animated Practical — Moving Coil Galvanometer
Magnetic Torque:
0.000 N m
Deflection:
0°
Observation:
Increasing current increases deflection.
📐 5. Derivation of Galvanometer Equation
For a coil of N turns, area A, carrying current I in magnetic field B:
τₘ = NABI
Restoring torque:
τᵣ = kθ
At equilibrium:
NABI = kθ
Hence:
⭐ I = kθ/NAB
Therefore:
⭐ θ = NAB/k × I
Thus:
Deflection is directly proportional to current.
🎯 6. Current Sensitivity
Current sensitivity is the deflection produced per unit current.
Current Sensitivity = θ/I
Using:
θ = NAB I/k
Therefore:
⭐ Sᵢ = θ/I = NAB/k
Current sensitivity can be increased by:
- Increasing number of turns N
- Increasing area A
- Increasing magnetic field B
- Decreasing torsional constant k
⚡ 7. Voltage Sensitivity
Voltage sensitivity is deflection produced per unit potential difference.
Voltage Sensitivity = θ/V
Since:
V = IG
where G is the galvanometer resistance.
Therefore:
⭐ Sᵥ = θ/V
Sᵥ = NAB/kG
Hence:
⭐ Voltage sensitivity = Current sensitivity / Resistance
📊 8. Current Sensitivity vs Voltage Sensitivity
| Current Sensitivity |
Voltage Sensitivity |
| θ/I |
θ/V |
| NAB/k |
NAB/kG |
| Depends on current |
Depends on voltage and resistance |
🔴 9. Conversion of Galvanometer into Ammeter
A galvanometer can be converted into an ammeter by connecting a
low resistance shunt S in parallel with it.
Let:
- G = resistance of galvanometer
- Ig = current required for full-scale deflection
- I = desired ammeter range
- S = shunt resistance
Since galvanometer and shunt are in parallel:
I₉G = (I − I₉)S
Therefore:
⭐ S = I₉G/(I − I₉)
✔ Ammeter = Galvanometer + Low Resistance Shunt in Parallel
🔬 10. Animated Ammeter Conversion
The shunt provides an alternate low-resistance path so that only a small
fraction of the total current passes through the galvanometer.
I = I₉ + Iₛ
Iₛ = I − I₉
🔵 11. Conversion of Galvanometer into Voltmeter
A galvanometer is converted into a voltmeter by connecting a
high resistance R in series with it.
Let:
- G = galvanometer resistance
- Ig = full-scale current
- V = desired voltmeter range
- R = series resistance
Using Ohm's law:
V = I₉(G + R)
Therefore:
⭐ R = V/I₉ − G
✔ Voltmeter = Galvanometer + High Resistance in Series
📋 12. Ammeter vs Voltmeter
| Feature |
Ammeter |
Voltmeter |
| Connection |
Series |
Parallel |
| Internal Resistance |
Very Low |
Very High |
| Conversion |
Low resistance shunt |
High resistance in series |
| Measures |
Current |
Potential difference |
📝 13. MCQ Practice
1. A moving coil galvanometer works on the principle that:
A. Current produces heat
B. Current-carrying coil in magnetic field experiences torque
C. Charge produces gravity
D. Resistance becomes zero
✔ Answer: B
2. The torque acting on a coil in a radial magnetic field is:
A. NABI
B. NAB/I
C. NI/AB
D. AB/NI
✔ Answer: A
3. Current sensitivity of a galvanometer is:
A. I/θ
B. θ/I
C. θV
D. I/V
✔ Answer: B
4. Current sensitivity is given by:
A. NAB/k
B. k/NAB
C. NABk
D. kG/NAB
✔ Answer: A
5. To convert a galvanometer into an ammeter, we connect:
A. High resistance in series
B. Low resistance in parallel
C. High resistance in parallel
D. Capacitor in series
✔ Answer: B
6. To convert a galvanometer into a voltmeter, we connect:
A. Low resistance in parallel
B. High resistance in series
C. Low resistance in series
D. No resistance
✔ Answer: B
7. An ideal ammeter has:
A. Very high resistance
B. Zero resistance
C. Infinite resistance
D. High capacitance
✔ Answer: B
8. An ideal voltmeter has:
A. Zero resistance
B. Very low resistance
C. Infinite resistance
D. Zero voltage
✔ Answer: C
9. Voltage sensitivity is:
A. θ/V
B. V/θ
C. I/θ
D. θI
✔ Answer: A
10. Increasing the number of turns of the coil:
A. Decreases current sensitivity
B. Increases current sensitivity
C. Has no effect
D. Makes resistance zero
✔ Answer: B
🟣 14. Assertion–Reason — 5 Questions
Options:
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, but R is not the correct explanation of A.
C. A is true, but R is false.
D. A is false, but R is true.
Assertion:
The deflection of a moving coil galvanometer is proportional to current.
Reason:
In a radial magnetic field, magnetic torque is proportional to current.
Answer: A
Assertion:
A galvanometer is converted into an ammeter by connecting a low
resistance in parallel.
Reason:
The shunt allows most of the current to bypass the galvanometer.
Answer: A
Assertion:
A galvanometer is converted into a voltmeter by connecting a high
resistance in series.
Reason:
The high series resistance limits the current through the galvanometer.
Answer: A
Assertion:
The current sensitivity increases when the torsional constant increases.
Reason:
Current sensitivity is NAB/k.
Answer: D
Assertion:
An ideal ammeter has zero resistance.
Reason:
It is connected in series with the circuit.
Answer: B
🟢 15. 2 Marks — 6 Questions
Q1
State the working principle of a moving coil galvanometer.
Q2
Write the expression for magnetic torque acting on the coil.
Q3
Define current sensitivity of a galvanometer.
Q4
Define voltage sensitivity of a galvanometer.
Q5
How is a galvanometer converted into an ammeter?
Q6
How is a galvanometer converted into a voltmeter?
🟡 16. 3 Marks — 6 Questions
Q1
Explain the working principle of a moving coil galvanometer.
Q2
Derive the relation θ = NAB I/k.
Q3
Derive the expression for current sensitivity.
Q4
Explain why a radial magnetic field is used in a moving coil galvanometer.
Q5
Explain the role of the soft iron core in a moving coil galvanometer.
Q6
Explain the difference between current sensitivity and voltage sensitivity.
🟠 17. 4 Marks — 6 Questions
Q1
Derive the equation of a moving coil galvanometer and explain its terms.
Q2
Derive the expression for current sensitivity of a galvanometer.
Q3
Derive the expression for voltage sensitivity.
Q4
Explain the conversion of a galvanometer into an ammeter and derive the
expression for shunt resistance.
Q5
Explain the conversion of a galvanometer into a voltmeter and derive the
expression for series resistance.
Q6
Explain why an ammeter has low resistance whereas a voltmeter has high
resistance.
🔴 18. 5 Marks — 6 Questions
Q1
Explain the construction and working of a moving coil galvanometer with
a neat labelled diagram.
Q2
Derive the relation between current and angular deflection in a moving
coil galvanometer.
Q3
Define current sensitivity and explain the factors affecting it.
Q4
Derive the expression for shunt resistance required to convert a
galvanometer into an ammeter of desired range.
Q5
Derive the expression for resistance required to convert a galvanometer
into a voltmeter of desired range.
Q6
Explain current sensitivity and voltage sensitivity and derive the
relation between them.
🔵 19. 6 Marks — 6 Questions
Q1
Describe the construction and working principle of a moving coil
galvanometer and derive its equation.
Q2
Derive the expression for current sensitivity and discuss how it can be
increased.
Q3
Derive the expression for voltage sensitivity and establish its relation
with current sensitivity.
Q4
Explain the conversion of a galvanometer into an ammeter. Derive the
formula for shunt resistance and explain the circuit arrangement.
Q5
Explain the conversion of a galvanometer into a voltmeter. Derive the
formula for series resistance and explain the circuit arrangement.
Q6
A galvanometer has resistance G and gives full-scale deflection for
current I₉. Derive expressions for converting it into an ammeter of range
I and a voltmeter of range V.
🧮 20. Numerical Practice
Numerical 1 — Ammeter Conversion
A galvanometer has resistance:
G = 100 Ω
Full-scale current:
I₉ = 1 mA
It is to be converted into an ammeter of range:
I = 1 A
Required shunt:
S = I₉G/(I − I₉)
S =
(0.001 × 100)/(1 − 0.001)
⭐ S ≈ 0.100 Ω
✔ Answer: Approximately 0.10 Ω
Numerical 2 — Voltmeter Conversion
A galvanometer has resistance 100 Ω and full-scale current 1 mA.
Find the resistance required to convert it into a 10 V voltmeter.
R = V/I₉ − G
R = 10/0.001 − 100
⭐ R = 9900 Ω
✔ Answer: 9.9 kΩ
📚 21. Important Formula Sheet
Magnetic torque:
τ = NABI
Restoring torque:
τ = kθ
Galvanometer equation:
θ = NABI/k
Current sensitivity:
Sᵢ = θ/I = NAB/k
Voltage sensitivity:
Sᵥ = θ/V = NAB/kG
Ammeter shunt:
S = I₉G/(I − I₉)
Voltmeter series resistance:
R = V/I₉ − G
🚀 22. Quick Revision
⚙️ Principle
Current-carrying coil in magnetic field experiences torque.
🎯 Current Sensitivity
Sᵢ = θ/I = NAB/k
⚡ Voltage Sensitivity
Sᵥ = θ/V
🔴 Ammeter
Low resistance shunt connected in parallel.
🔵 Voltmeter
High resistance connected in series.
🧲 Radial Field
Ensures maximum and uniform torque.
