A de motor is connected to a constant emf of 12.0 V. The resistance of its windings is 2.0 Ω. At

step 1 Hi, in the given problem, voltage supply to the motor is V is equal to 12 .0 volt. Resistance of

A de motor is connected to a constant emf of 12.0 V. The...

A de motor is connected to a constant emf of $12.0 \mathrm{V}$. The resistance of its windings is $2.0 \Omega .$ At normal operating speed, the motor takes in $6.0 \mathrm{W}$ of electrical power. (a) What is the initial current drawn by the motor when it is first started up? (b) What current does it draw at normal operating speed? (c) What is the back emf induced in the windings at normal speed?

Key Concepts

Transient vs. Steady-State Behavior in Electric Motors

This concept differentiates between the motor's behavior at the moment of start-up (transient state) and during normal operation (steady-state). At start-up, the rotor is stationary and no back emf is present, leading to a high current draw determined solely by the applied voltage and winding resistance. In steady-state operation, the back emf reduces the net voltage across the windings, resulting in a lower current draw even though the applied voltage remains constant.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that defines the relationship between voltage, current, and resistance (V = I × R). It allows us to calculate any one of these three variables when the other two are known, which is essential for analyzing how an electric motor behaves under different conditions, such as at start-up compared to normal operation.

Electrical Power in Resistive Circuits

The electrical power consumed by a resistive element is given by the equation P = I²R. This concept is used to determine how much power is being dissipated as heat in the motor’s windings and is crucial for understanding how the operating current is affected by resistive losses in the circuit.

Back Electromotive Force (Back emf)

Back electromotive force (back emf) is the voltage generated in a running motor that opposes the applied voltage. As the motor speeds up, the back emf increases, reducing the net voltage across the motor windings and thus the current drawn from the power source. This concept is key to understanding why the initial current draw of a motor (when there is no back emf) is much higher than its steady-state operating current.

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