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The simple rotating loop between pole faces connected to a battery and resistor through a switch, the specifications of this machine are radius = 0.5m, length 1m, resistance = 0.3 ohms and magnitude strength = 0.25T is supplied with 120V. What is the steady state angular velocity at no-load?
- a)480 rad/s
- b)960 rad/s
- c)320 rad/s
- d)490 rad/s
Correct answer is option 'A'. Can you explain this answer?
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The simple rotating loop between pole faces connected to a battery and...
v = V/(2*r*l*B)
= 120/(2*0.0005*1*0.25)
= 480 rad/s.
= 120/(2*0.0005*1*0.25)
= 480 rad/s.
Most Upvoted Answer
The simple rotating loop between pole faces connected to a battery and...
To find the steady-state angular velocity at no-load, we can use the principle of conservation of energy and the concept of electromagnetic induction. Let's break down the problem into different parts and find the solution step by step.
1. Calculation of Back EMF:
- The magnetic field strength is given as 0.25T.
- The length of the loop is given as 1m.
- The speed of the loop is constant at no-load, so we can consider it as the angular velocity (ω).
- The induced electromotive force (EMF) is given by the formula: EMF = B*L*ω, where B is the magnetic field strength and L is the length of the loop.
- Therefore, the back EMF in the loop is: EMF = (0.25T) * (1m) * ω = 0.25ω V.
2. Calculation of Voltage across the Resistor:
- The resistance of the loop is given as 0.3 ohms.
- The current flowing through the loop is given by Ohm's Law: I = V/R, where V is the voltage supplied and R is the resistance.
- Therefore, the current flowing through the loop is: I = 120V / 0.3 ohms = 400A.
- The voltage across the resistor is given by: V_resistor = I * R = 400A * 0.3 ohms = 120V.
3. Calculation of Voltage across the Loop:
- The voltage supplied is given as 120V.
- The voltage across the loop is the sum of the back EMF and the voltage across the resistor: V_loop = EMF + V_resistor.
- Therefore, V_loop = 0.25ω V + 120V.
4. Calculation of Steady-State Angular Velocity:
- At no-load, the current flowing through the loop is zero, i.e., I = 0A.
- Therefore, the voltage across the resistor is zero, i.e., V_resistor = 0V.
- Substituting these values into the equation V_loop = 0.25ω V + 120V, we get: 0 = 0.25ω V + 120V.
- Solving this equation for ω, we find: 0.25ω = -120V.
- ω = -120V / 0.25 = -480 rad/s.
Since angular velocity cannot be negative, the steady-state angular velocity at no-load is 480 rad/s (option A).
1. Calculation of Back EMF:
- The magnetic field strength is given as 0.25T.
- The length of the loop is given as 1m.
- The speed of the loop is constant at no-load, so we can consider it as the angular velocity (ω).
- The induced electromotive force (EMF) is given by the formula: EMF = B*L*ω, where B is the magnetic field strength and L is the length of the loop.
- Therefore, the back EMF in the loop is: EMF = (0.25T) * (1m) * ω = 0.25ω V.
2. Calculation of Voltage across the Resistor:
- The resistance of the loop is given as 0.3 ohms.
- The current flowing through the loop is given by Ohm's Law: I = V/R, where V is the voltage supplied and R is the resistance.
- Therefore, the current flowing through the loop is: I = 120V / 0.3 ohms = 400A.
- The voltage across the resistor is given by: V_resistor = I * R = 400A * 0.3 ohms = 120V.
3. Calculation of Voltage across the Loop:
- The voltage supplied is given as 120V.
- The voltage across the loop is the sum of the back EMF and the voltage across the resistor: V_loop = EMF + V_resistor.
- Therefore, V_loop = 0.25ω V + 120V.
4. Calculation of Steady-State Angular Velocity:
- At no-load, the current flowing through the loop is zero, i.e., I = 0A.
- Therefore, the voltage across the resistor is zero, i.e., V_resistor = 0V.
- Substituting these values into the equation V_loop = 0.25ω V + 120V, we get: 0 = 0.25ω V + 120V.
- Solving this equation for ω, we find: 0.25ω = -120V.
- ω = -120V / 0.25 = -480 rad/s.
Since angular velocity cannot be negative, the steady-state angular velocity at no-load is 480 rad/s (option A).
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The simple rotating loop between pole faces connected to a battery and resistor through a switch, the specifications of this machine are radius = 0.5m, length 1m, resistance = 0.3 ohms and magnitude strength = 0.25T is supplied with 120V. What is the steady state angular velocity at no-load?a)480 rad/sb)960 rad/sc)320 rad/sd)490 rad/sCorrect answer is option 'A'. Can you explain this answer?
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