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Qwestrum Engineering360 · Electrical & Electronics · Electrical Machines – I

DC Motor Characteristics

A DC motor develops torque T = KΦI_a and runs at a speed set by N ∝ (V − I_aR_a)/Φ; the field connection makes the shunt motor a constant-speed drive and the series motor a high-starting-torque drive.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Shunt motor: approximately constant speed
  • Series motor: high starting torque; never no-load
  • Speed control: armature voltage (below base) and field weakening (above base)

Topic details

Introduction

The back EMF E = V − I_aR_a is central: it limits armature current automatically as the motor speeds up. At starting E = 0, so a starter resistance is needed to keep inrush current within limits.

Scope in B.Tech and GATE syllabus

The two characteristic families are torque–armature-current and speed–armature-current. Series motors give T ∝ I_a² (huge starting torque, used in traction) but must never run at no load, where flux collapses and speed runs away. Shunt motors hold nearly constant speed.

Key relations & formulas

E=V−IaRaE = V - I_{a} R_{a}
(back emf)
T=KΦIaT = K \Phi I_{a}
(electromagnetic torque)
N∝(V−IaRa)ΦN ∝ \frac{(V - I_{a} R_{a})}{\Phi}
(speed equation)

Notation and sign conventions

Relation 1 —
E=V−IaRaE = V - I_{a} R_{a}
E=V−IaRaE = V - I_{a} R_{a}
(back emf)
Write this relation with symbols exactly as in Electrical Machines — Nagrath & Kothari before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
T=KΦIaT = K \Phi I_{a}
T=KΦIaT = K \Phi I_{a}
(electromagnetic torque)
Write this relation with symbols exactly as in Electrical Machines — Nagrath & Kothari before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
N∝N ∝
N∝(V−IaRa)ΦN ∝ \frac{(V - I_{a} R_{a})}{\Phi}
(speed equation)
Write this relation with symbols exactly as in Electrical Machines — Nagrath & Kothari before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

Speed control below base speed uses armature-voltage control (reduce V, keeping Φ constant) which keeps torque capability; above base speed uses field weakening (reduce Φ) which reduces available torque but raises speed.

Governing relations in practice

For a shunt motor Φ is nearly constant, so N ∝ E = V − I_aR_a; the small drop I_aR_a explains the slight speed fall on load. Ward-Leonard control varies armature voltage over a wide range.

Design and analysis considerations

When comparing two operating points of the same machine, use N₁/N₂ = (E₁/E₂)(Φ₂/Φ₁) to avoid needing the machine constant K.

Assumptions and validity limits

State assumptions explicitly before using any relation for dc motor characteristics — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Electrical Machines I viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Electrical Machines I papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to dc motor characteristics.
4. Use equation 1:
E=V−IaRaE = V - I_{a} R_{a}
.
5. Use equation 2:
T=KΦIaT = K \Phi I_{a}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

DC Motor Characteristics appears in substations, drives, and labs. In Indian electrical curricula this topic is tested because it connects theory to magnetic circuits, transformers, and DC machines.
GATE and semester exams often combine dc motor characteristics with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use dc motor characteristics?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Using V instead of back EMF E in the speed ratio formula
• Forgetting the I_aR_a drop when computing speed on load
• Assuming a series motor can be belt-decoupled and run at no load (dangerous overspeed)
• Keeping Φ constant while doing field-weakening speed control

Quick revision checklist

Before attempting dc motor characteristics problems, confirm you can:
1. Shunt motor: approximately constant speed
2. Series motor: high starting torque; never no-load
3. Speed control: armature voltage (below base) and field weakening (above base)
Revise the solved examples in Electrical Machines — Nagrath & Kothari and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Speed of a shunt motor on load

Problem

A 220 V DC shunt motor draws an armature current of 20 A and runs at 1000 rpm; R_a = 0.5 Ω. Find the speed when the armature current rises to 40 A (flux constant).

Solution

E₁ = V − I_a₁R_a = 220 − 20×0.5 = 210 V.
E₂ = 220 − 40×0.5 = 200 V.
Flux constant → N₂/N₁ = E₂/E₁ = 200/210.
N₂ = 1000 × 200/210 = 952 rpm.

Conceptual check — DC Motor Characteristics

Problem

In a Electrical Machines I semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of dc motor characteristics." What should a complete answer include?

Exams & GATE

Nagrath & Kothari — plot torque-speed and efficiency curves.

📖 Standard books (India)

  • Electrical Machines — Nagrath & Kothari

    Read: Syllabus unit

    Transformers, DC machines, and induction motors

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