Question

What does $R_a$ indicate in the voltage equation $V=E_{b}+I_{a}R_{a}$ of DC motor?}

• A. Input voltage
• B. Back emf
• C. Armature current
• D. Armature resistance

Hint:

The armature winding has a very low resistance ($R_a < 1\,\Omega$) to minimize $I_a^2 R_a$ copper losses and voltage drops. Under starting conditions, since back emf $E_b \propto N$ (speed) is zero, starter resistors are used to limit the starting current $I_s = V / R_a$.

Answer 1

The Correct Option is D

Step 1: Understanding the DC Motor Voltage Equation:
The fundamental voltage balance equation of a DC motor is given by: $$V = E_b + I_a R_a$$

Step 2: Identifying the Mathematical Terms:
Let us define each mathematical term within this electrical equation:

• $V$: The terminal input DC voltage applied across the motor terminals (measured in Volts).
• $E_b$: The Counter-Electromotive Force or Back emf induced in the armature conductor as it rotates in the magnetic field (measured in Volts). It is given by $E_b = \frac{\Phi Z N P}{60 A}$.
• $I_a$: The current flowing through the armature conductors, known as the Armature Current (measured in Amperes).
• $R_a$: The electrical resistance offered by the copper conductors of the armature winding, called the Armature Resistance (measured in Ohms, $\Omega$).
• $I_a R_a$: The total resistive voltage drop occurring across the armature winding.

Step 3: Conclusion:
Therefore, $R_a$ represents the armature resistance, making option (D) the correct answer.