Electric Generators, Induced EMF, Electromagnetic Induction - Physics

TL;DR

Electric-generator problems are solved by finding angular speed with ω = 2πf, peak EMF with NBAω, RMS voltage by dividing peak voltage by √2, and current with V/R. For the first worked AC-generator calculation, 60 Hz gives 377 radians per second and a peak output of 282.75 volts. Read on for formulas, substitutions, and a second example covering frequency and resistor power.

Transcript

in this video we're going to focus on solving some common physics problems associated with electric generators so in this problem we have a 60 hertz ac generator and this generator has a coil with an area of 5 times 10 to the minus 3 square meters and the number of loops is 500 and we're given the strength of the magnetic field inside this generato... Read More

Key Insights

• 🤨 The angular speed of an AC generator can be calculated by multiplying 2 pi by the frequency.
• 🙊 The peak output voltage of an AC generator can be determined using the formula nba times omega.
• ⚡ The rms voltage produced by the generator can be found by dividing the peak voltage by the square root of two.
• 🤒 The rms current flowing in a resistor connected to the generator can be calculated by dividing the rms voltage by the resistance.
• ✊ Power dissipated by the resistor can be determined using the formula i squared times r.
• 🤨 The angular speed of an AC generator can be converted from rpm to radians per second by multiplying by 2 pi and dividing by 60.
• 🤨 The frequency of an AC generator can be calculated by dividing the angular speed by 2 pi.

Questions & Answers

Q: How do you calculate the angular speed of an AC generator from frequency?

Use ω = 2πf, where f is the frequency. For the 60-hertz generator, 2π × 60 gives approximately 377 radians per second.

Q: How do you calculate the peak induced EMF of an AC generator?

Use the peak-output formula NBAω, where N is the number of loops, B is magnetic-field strength, A is coil area, and ω is angular speed. In the first worked substitution, 1500 loops, 0.10 tesla, 0.005 square meters, and 377 radians per second produce 282.75 volts.

Q: How do you calculate an AC generator's RMS voltage?

Divide the peak voltage by the square root of two. A peak voltage of 282.75 volts therefore gives an RMS voltage of approximately 199.9 volts.

Q: What RMS current flows through a 50-ohm resistor connected to the generator?

Use I = V/R with the RMS voltage. Dividing 199.9 volts by 50 ohms gives 3.998 amps, which rounds to 4 amps.

Q: How do you convert generator speed from rpm to radians per second?

Multiply the rotational speed by 2π radians per revolution and divide by 60 seconds per minute. Applying this conversion to 2500 rpm gives 261.8 radians per second.

Q: How do you calculate generator frequency from angular speed?

Rearrange ω = 2πf to get f = ω/(2π). An angular speed of 261.8 radians per second gives a frequency of 41.67 hertz.

Q: What peak voltage and RMS current are produced in the second generator example?

For 200 loops, a 0.25-tesla field, a circular coil with a 0.10-meter radius, and an angular speed of 261.8 radians per second, NBAω gives a peak voltage of 411.2 volts. Across a 100-ohm resistor, the peak current is 4.112 amps, and dividing by √2 gives an RMS current of 2.908 amps.

Q: How much average power does the 100-ohm resistor dissipate?

Use the RMS relation P = I²R. With an RMS current of 2.908 amps and resistance of 100 ohms, the average dissipated power is 845.6 watts; the alternative peak-current calculation gives about 845.4 watts because of rounding.

Summary & Key Takeaways

• The video discusses how to calculate the angular speed of an AC generator based on the frequency, area of the coil, number of loops, and strength of the magnetic field.

• It explains how to determine the peak output voltage of an AC generator by using the formula nba times omega, where n is the number of loops, b is the strength of the magnetic field, a is the area of the coil, and omega is the angular speed.

• The video also covers how to calculate the rms voltage produced by the generator by dividing the peak voltage by the square root of two.

• Additionally, it provides instructions on calculating the rms current flowing in a resistor when connected to the generator and determines the power dissipated by the resistor using the formula i squared times r.