GATE Electrical Engineering - Complete Master Library

 

📘 DC Machine – Torque Equation & Derivation

Torque equation is derived from power balance between electrical and mechanical systems. Very important for GATE and interviews.

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🔹 1. Electrical Power Converted

Electrical power converted into mechanical form:

P_mech = E × I_a

Where: E = Back EMF I_a = Armature current

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🔹 2. Mechanical Power

Mechanical power:

P_mech = T × ω

Where: T = Torque (Nm) ω = Angular speed (rad/s)

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🔹 3. Equating Both

E I_a = T ω

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🔹 4. Substitute EMF Equation

We know:

E = (P Φ Z N) / (60 A)

Angular speed:

ω = 2πN / 60

Substitute into power equation and simplify.

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🔹 5. Final Torque Equation

After simplification:

T = (P Z Φ I_a) / (2π A)

Or,

T ∝ Φ I_a

Most important result.

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🔹 6. Example

Given: P = 4 Z = 600 Φ = 0.015 Wb I_a = 50 A Wave winding → A = 2 Calculate torque. Solution:

T = (4 × 600 × 0.015 × 50) / (2π × 2)

Step-by-step: Numerator = 4 × 600 × 0.015 × 50 = 1800 Denominator ≈ 12.57

T ≈ 143.2 Nm

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🔹 7. Important Observations

• Torque proportional to flux
• Torque proportional to armature current
• Independent of speed directly
• Used in speed control analysis

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🎯 GATE Important Points

• Remember T ∝ Φ I_a
• Used in motor characteristic derivation
• Foundation for DC motor types
• Often asked in derivation form

Torque = Magnetic Interaction Force