Which of the following formulas is used to find the value of different Stud resistance in DC Series motor?

Question

Examoogle · Accepted Answer

Option C: $R_n = \gamma R_{n-1} - \frac{V}{I_1}(\beta - 1)$

Explanation & Concepts:
In a DC series motor starter, the total starter resistance is divided into sections connected between successive studs to limit starting current. The resistance of the $n^{	ext{th}}$ stud section is given by $R_n = \gamma R_{n-1} - \frac{V}{I_1}(\beta - 1)$, where $\gamma$ and $\beta$ are current and speed ratios during starting. This formula governs the step-by-step resistance required for smooth acceleration.

Working Principle: When a DC series motor starts, back EMF ($E_b$) is zero, resulting in extremely high armature current if unmonitored. A graded starter resistance is gradually cut out as speed increases and back EMF builds up. The upper current limit ($I_1$) and lower current limit ($I_2$) define the switching ratio $\beta = I_1 / I_2$, which dictates the resistance values for each stud to ensure current remains within safe limits.

Key Formulas: $R_n = \gamma R_{n-1} - \frac{V}{I_1}(\beta - 1)$ — Resistance of the $n^{	ext{th}}$ stud step for DC series motor starter; $\beta = \frac{I_1}{I_2}$ — Ratio of upper current limit to lower current limit; $I_1 = \frac{V - E_b}{R_1}$ — Peak starting current at stud contact

Key Points: Unlike shunt motors, flux in a DC series motor varies with armature current, altering back EMF ratio parameters during starting.; The parameter $\gamma$ accounts for flux non-linearity and speed variation between switching steps.; Stud resistance calculation ensures current fluctuates smoothly between $I_1$ and $I_2$ to prevent torque dips and winding damage.

Advantages: Prevents severe voltage dips in the supply network during motor startup.; Ensures smooth mechanical acceleration without high mechanical stress on the shaft.

Disadvantages: Significant power dissipation in external resistor studs during acceleration.; Complex calculation compared to DC shunt motor starters due to variable field flux.

Applications: Design of multi-step drum starters for electric traction systems.; Manual and automatic contactor starters for series motor crane drives.

Additional Info: Option A ($R_n = r_n - R_{n+1}$) represents simple series resistance subtraction, which is incomplete for starter design.. Option B ($R_n = \gamma^{n-1} R_1$) applies to DC shunt motor starters where field flux remains constant.

Answer: C is correct — The formula for stud resistance in a DC series motor includes the field flux variability factor $\gamma$ and current ratio $\beta$, given by $R_n = \gamma R_{n-1} - \frac{V}{I_1}(\beta - 1)$.

Exam Tip: Remember: DC shunt motor stud resistances form a geometric progression because flux is constant, whereas DC series motor starter design requires adjusting for variable flux via additional factor terms.

Examoogle · Answer

Option A: $R_n = r_n - R_{n+1}$

Examoogle · Answer

Option B: $R_n = \gamma^{n-1} R_1$

Examoogle · Answer

Option D: All of these

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