A 20 hp, 230 V dc series motor draws 64 A when the speed is 56 r / s. If Ra=0.12 Ωand Rs=0.06

step 1 So, we know torque is directly proportional to current and magnetic field strength. So, tau is d

A 20 hp, 230 V dc series motor draws 64 A when the speed...

A $20 \mathrm{hp}, 230 \mathrm{~V}$ dc series motor draws $64 \mathrm{~A}$ when the speed is $56 \mathrm{r} / \mathrm{s}$. If $R_a=0.12 \Omega$ and $R_s=0.06 \Omega$, determine the speed when the line current is $84 \mathrm{~A}$.

Key Concepts

Voltage Equation in DC Motors

The fundamental voltage equation in DC motors relates the applied voltage to the sum of the voltage drops across the internal resistances and the back EMF. In the case of a series motor, the equation is V = I*(R_a + R_s) + E, where I is the current, R_a and R_s are the armature and series resistances respectively, and E is the back EMF. This equation forms the basis for analyzing motor performance under different operating conditions.

Back EMF (Electromotive Force)

The back EMF in a DC motor is the voltage induced in the armature windings as a result of its rotation in the magnetic field. This induced voltage opposes the applied voltage and is proportional to the motor speed and the magnetic flux. It plays a crucial role in the motor’s equilibrium as it regulates the current drawn by the motor, especially under varying load conditions.

Speed-Torque Relationship in DC Motors

The speed-torque characteristic of a DC series motor is derived from its voltage and current relationships. As the load and current change, both the generated flux and the back EMF vary, leading to a change in speed. Understanding this relationship is key to determining how changes in current or load can affect the motor’s operating speed, particularly when solving for unknown speeds under different current conditions.

DC Series Motor

DC series motors are characterized by having their armature and field windings connected in series, meaning that the same current flows through both. This configuration results in high starting torque, making them well suited for applications requiring heavy load acceleration. The motor’s speed and torque are interdependent, as the magnetic flux generated by the field winding is directly related to the armature current.

Armature and Field Resistance

In a DC series motor, internal resistances such as the armature resistance and the series field resistance are critical in determining the voltage drops within the motor. These resistances affect the available voltage for producing the back electromotive force (EMF), and consequently influence the motor’s speed and torque. Properly accounting for both resistances is essential in accurate performance and speed calculations.

Please give Ace some feedback