Which of the following formulas is used to find the value of different section resistance in the DC Series mot

Question

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

Examoogle · Accepted Answer

Option B: $r_n = \gamma^{n-1} r_1$

Explanation & Concepts:
In DC series motor starters, resistance sections are designed such that the upper limit of current at each stud remains constant. To achieve this, the resistance values of consecutive sections follow a geometric progression governed by a constant ratio $\gamma$.

Working Principle: When a DC series motor is started, high starting current is controlled by stepping down resistance across multiple studs. The ratio of total circuit resistance at consecutive studs is kept constant as $\gamma = \frac{R_n}{R_{n-1}}$, which yields the resistance of the $n$-th section as $r_n = \gamma^{n-1} r_1$.

Key Formulas: $r_n = \gamma^{n-1} r_1$ — resistance of $n$-th section in DC series motor starter; $\gamma = \left(\frac{R_m}{R_1}\right)^{\frac{1}{n}}$ — resistance ratio constant; $R_1 = \frac{V}{I_{max}}$ — total initial resistance at starting

Key Points: The section resistances in a DC series motor starter form a Geometric Progression (GP).; $\gamma$ is the ratio of successive total resistance values during the starting process.; The constant ratio ensures maximum current limit remains uniform across all studs.

Advantages: Ensures uniform current peaks during motor acceleration.; Prevents thermal damage to armature windings by controlling starting current step-by-step.

Disadvantages: Power loss occurs across resistance sections during starting phase.

Applications: Design of starters for DC series motors used in traction and cranes.

Additional Info: Option A ($r_n = \alpha^{n-1} r_1$) is commonly used for DC shunt motor starters where $\alpha$ represents the resistance ratio factor under constant flux conditions.. Option C ($r_n = \alpha r_{n-1}$) relates adjacent total resistance sections directly rather than step section resistance.

Answer: B is correct — The resistance of the $n$-th section in a DC series motor starter is given by $r_n = \gamma^{n-1} r_1$ where $\gamma$ is the resistance ratio.

Exam Tip: Remember: DC Shunt Motor starter design typically uses $\alpha$ assuming constant flux, whereas DC Series Motor starter design accounts for varying flux and uses $\gamma$.

Examoogle · Answer

Option A: $r_n = \alpha^{n-1} r_1$

Examoogle · Answer

Option C: $r_n = \alpha r_{n-1}$

Examoogle · Answer

Option D: All of these

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)