Question

A universal series motor when connected to a 220 V dc draws 10 a and runs at 1400 rpm. Find new speed and power factor when connected to 220v, 25 hz supply the motor current remaining Same. the motor has total resistance of 1 ohm and total inductance of 0.1 H​

Answer 1

Answer:

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Answer 2

Answer:

The  new speed and the power factor is given by $\begin{aligned}&N_{a c}=960.73 \mathrm{rpm} \\&\cos (\phi)=0.7(\mathrm{lag})\end{aligned}$

Explanation:

Given: A universal series motor, when operating on 220 V DC draws 10 A and runs at 1400 rpm and when connected to 220 V, 25 Hz supply, the motor current remains the same. The motor has a total resistance of 1 ohm and total inductance of 0.1 H.

To find: The current

Solution:

According to the question:

When motor is operating on DC,

$\begin{aligned}&\because E_{d c}=V_{d c}-I_{a} R \\&\Rightarrow E_{d c}=220-10 \times 1 \\&\Rightarrow E_{d c}=210 \mathrm{~V}\end{aligned}$

When motor is operating on $A C$,

$\begin{aligned}&\because X=2 \pi \mathrm{fL} \\&\Rightarrow X=2 \times 3.14 \times 25 \times 0.1 \\&\Rightarrow X=15.7 \Omega \\&\because E_{a c}+I_{a} R=\sqrt{V_{a c}^{2}-\left(I_{a} X\right)^{2}} \\&\Rightarrow E_{a c}+10 \times 1=\sqrt{220^{2}-(10 \times 15.7)^{2}} \\&\Rightarrow E_{a c}+10=154.11 \\&\Rightarrow E_{a c}=144.11 \mathrm{~V}\end{aligned}$

Since the current is same in both the case so flux will be equal in both the case.

$\therefore \phi_{d c}=\phi_{a c}$

The speed when ac supply is connected to the motor is calculated as

$\because E_{d c}=k \phi_{d c} N_{d c} \ldots \ldots(1) \\\ E_{a c}=k \phi_{a c} N_{a c} \ldots \ldots \ldots(2)$

$\therefore \frac{E_{d c}}{E_{a c}}=\frac{N_{d c}}{N_{a c}}$

$\Rightarrow \frac{210}{144.11}=\frac{1400}{N_{a c}} \\ \Rightarrow N_{a c}=960.73 \mathrm{rpm}$

The power factor is calculated as

$\because \cos (\phi)=\frac{E_{a c}+I_{a} R}{V_{a c}}$

$\Rightarrow \cos (\phi)=\frac{144.11+10 \times 1}{220}$

$\Rightarrow \cos (\phi)=0.7\text{lag}$

Answers are

$\begin{aligned}&N_{a c}=960.73 \mathrm{rpm} \\&\cos (\phi)=0.7(\mathrm{lag})\end{aligned}$