A) Decreases
B) Increases
C) Remains same
D) None of the above
✅ Answer: B) Increases
💡 Detailed Explanation
In a DC shunt motor, the field winding is connected across the supply voltage. When the temperature of the motor increases, the resistance of the copper field winding also increases.
The resistance of a winding changes with temperature according to:
Rₜ = R₀ [1 + α(T − T₀)]
Where:
Rₜ = Resistance at temperature T
R₀ = Resistance at reference temperature T₀
α = Temperature coefficient of resistance
T = Final temperature
T₀ = Initial temperature
Therefore:
Temperature ↑ → Field resistance Rf ↑
🔹 Step 1: Effect on Field Current
The field current of a DC shunt motor is:
If = V / Rf
Since the supply voltage V is approximately constant, an increase in field resistance causes the field current to decrease.
Therefore:
Rf ↑ → If ↓
🔹 Step 2: Effect on Magnetic Flux
For a DC shunt motor, the magnetic flux is approximately proportional to the field current, particularly before magnetic saturation.
Φ ∝ If
Therefore:
If ↓ → Φ ↓
So, when the motor temperature increases, the field flux tends to decrease.
🔹 Step 3: Effect on Motor Speed
The back EMF of a DC motor is:
Eb = V − IaRa
The speed equation of a DC motor is approximately:
N ∝ Eb / Φ
or
N = K × Eb / Φ
where:
N = Motor speed
Eb = Back EMF
Φ = Magnetic flux
K = Motor constant
When the field flux decreases, the speed of the motor tends to increase.
Therefore:
Temperature ↑ → Rf ↑ → If ↓ → Φ ↓ → N ↑
Hence, the correct answer is:
✅ B) Increases
🔢 Numerical Example
Consider a DC shunt motor operating from a 220 V supply.
Initially, the field resistance is:
Rf₁ = 220 Ω
Therefore, the initial field current is:
If₁ = V / Rf₁
If₁ = 220 / 220
If₁ = 1 A
Now suppose the motor temperature increases and the field resistance becomes:
Rf₂ = 242 Ω
The new field current will be:
If₂ = V / Rf₂
If₂ = 220 / 242
If₂ ≈ 0.909 A
Thus:
Field resistance ↑ → Field current ↓
Since the field current decreases, the magnetic flux also decreases.
If ↓ → Φ ↓
Since:
N ∝ Eb / Φ
the motor speed tends to increase.
⚠️ Important Note
The armature resistance also increases when the motor temperature rises. This increases the armature voltage drop:
IaRa
and therefore tends to reduce the back EMF.
However, in this standard MCQ, the important effect being considered is the increase in shunt-field resistance, which reduces field current and flux. Hence, the expected answer is "Increases."
📌 Remember Points
| Condition | Effect |
|---|---|
| 🌡️ Temperature increases | ↑ |
| 🔌 Field resistance Rf | ↑ |
| ⚡ Field current If | ↓ |
| 🧲 Field flux Φ | ↓ |
| ⚙️ DC shunt motor speed N | ↑ |
🔥 Exam Shortcut
Temperature ↑ → Rf ↑ → If ↓ → Φ ↓ → Speed ↑
✅ Final Answer
B) Increases