(c) A separately excited d.c motor with a reactive feedback diode across it is fed from a [tex]$240 V, 50 Hz$[/tex] a.c supply through a single phase half-controlled bridge rectifier. The armature inductance and resistance are 0.06 H and [tex]$6 \Omega$[/tex] respectively. If the firing delay angle is [tex]$80^{\circ}$[/tex] and motor back e.m.f is 150 V , determine the mean input voltage of the d.c motor.
Answer (2)
The mean input voltage of the d.c motor is approximately 63.40 V , calculated using the maximum voltage from the AC supply and the given firing delay angle. The process involved converting the angle to radians and applying the appropriate formula for a half-controlled bridge rectifier. This mean voltage impacts the operation of the motor significantly.
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Convert the firing delay angle from degrees to radians: α = 8 0 ∘ = 1.396 radians .
Calculate the maximum voltage: V ma x = 2 × 240 ≈ 339.41 V .
Apply the formula for the mean input voltage: V m = 2 π V ma x ( 1 + cos ( α )) .
Calculate the mean input voltage: V m ≈ 63.40 V . The mean input voltage of the d.c motor is 63.40 V .
Explanation
Problem Setup We are given a separately excited d.c motor fed from a 240 V , 50 Hz a.c supply through a single phase half-controlled bridge rectifier. We need to determine the mean input voltage of the d.c motor, given the firing delay angle α = 8 0 ∘ .
Formula for Mean Input Voltage The mean input voltage V m of the d.c motor can be calculated using the formula for a single-phase half-controlled bridge rectifier: V m = 2 π V ma x ( 1 + cos ( α )) where V ma x = 2 × V r m s and V r m s = 240 V .
Convert Delay Angle to Radians First, we need to convert the firing delay angle α from degrees to radians: α r a d ian s = α d e g rees × 180 π α r a d ian s = 80 × 180 π ≈ 1.396 radians
Calculate Maximum Voltage Next, we calculate V ma x :
V ma x = 2 × 240 ≈ 339.41 V
Calculate Mean Input Voltage Now, we can calculate the mean input voltage V m :
V m = 2 π 339.41 ( 1 + cos ( 1.396 )) ≈ 2 π 339.41 ( 1 + ( − 0.1736 )) ≈ 2 π 339.41 ( 0.8264 ) ≈ 63.40 V
Final Answer Therefore, the mean input voltage of the d.c motor is approximately 63.40 V .
Examples
Understanding the mean input voltage of a DC motor controlled by a rectifier is crucial in various applications. For instance, in electric vehicles, the motor's speed and torque are directly influenced by this voltage. By adjusting the firing angle of the rectifier, we can control the power delivered to the motor, optimizing performance and efficiency. This principle also applies in industrial settings where DC motors drive machinery, and precise control over motor voltage is essential for accurate operation.
