A fan operates at $200 V$ (dc) consuming $1000 W$ when running at full speed. Its internal wiring has resistance $1 Ω$ . When the fan runs at full speed, its speed becomes constant. This is because the torque due to magnetic field inside the fan is balanced by the torque due to air resistance on the blades of the fan and the torque due to friction between the fixed part and the shaft of the fan. The electric power going into the fan is spent (i) in the internal resistance as heat, call it $P_{1}$ , (ii) in doing work against internal friction and air resistance producing heat, sound, etc., call it $P_{2}$ . When the coil of fan rotates, an emf is also induced in the coil. This opposes the external emf is also induced in the coil. This opposes the external emf applied to send the current to the fan. This emf is called back emf, call it $e$ . Answer the following questions when the fan is running at full speed.The current flowing into the fan and the value of back emf $e$ is

200 A, 5 V

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 A, 200 V

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 A, 195 V

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 A, 0 V

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $5 A, 195 V$
$E = 200 V, R = 1 Ω, P = P_{1} + P_{2} = 1000 W$

Current $I = \frac{P}{E} = \frac{1000}{200} = 5 A$

Back emf $e$ $= E - I R = 200 - 5 \times 1 = 195 V$

Suggest Corrections

Similar questions

A ceiling fan is rotating at the rate of $3.5 r p s$ and its moment of inertia is $1.25 k g m^{2}$ . If the current is switched off, the fan comes to rest in $5.5 s$ . The torque acting on the fan due to friction is:

Q. The circuit given below is for the operation of an industrial fan. The resistance of the fan is

3 o h m

. The regulator provided with the fan is a fixed resistor and a variable resistor in parallel. Under what value of the variable resistance given, power transferred to the fans will be maximum? The power source of the fan is a dc source with internal resistance of

6 o h m

Q. An electric fan runs from the 230 V mains. The current flowing through it is 0.4 A. At what rate is electrical energy transferred by the fan?

Q. A ceiling fan has a diameter of the circle through the outer edges of the three blades of

120 c m

and rpm

1500

at full speed. Consider a particle of mass

1 g

sticking at the outer end of the blade. What is the net force on it, when the fan runs at full speed? Who exerts this force on the particle? How much force does the particle exert on the blade in the plane of motion?

Q. A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of 120 cm and rpm 1500 at full speed. Consider a particle of mass 1 g sticking at the outer end of a blade. How much force does it experience when the fan runs at full speed? Who exerts this force on the particle? How much force does the particle exert on the blade along its surface?

Join BYJU'S Learning Program

The correct option is D 5A,195VE=200V,R=1Ω,P=P1+P2=1000WCurrent I=PE=1000200=5ABack emf e=E−IR=200−5×1=195V

The correct option is D $5 A, 195 V$
$E = 200 V, R = 1 Ω, P = P_{1} + P_{2} = 1000 W$

Current $I = \frac{P}{E} = \frac{1000}{200} = 5 A$

Back emf $e$ $= E - I R = 200 - 5 \times 1 = 195 V$