1. Electromagnetic Induction
AC Circuits and transformers

2. Effective Current
Emf in ac circuits is equivalent to potential difference in dc circuits
Resistance, current, and emf can all be measured using a multimeter
Induced emf as a function of time = maximum emf * sine of the angular frequency of rotation * time
Δv = Δvmax * sinω * t
Instantaneous current = maximum current * sine of the angular frequency of rotation * time
i = Imax * sinω * t

3. Effective Current

4. Effective Current
Since alternating current is constantly reversing, maximum current and emf values are not as useful as they are in direct current
Of more importance are instantaneous and root-mean-square (rms) values
Rms current – the amount of direct current that dissipates as much energy in a resistor as an instantaneous alternating current does during a complete cycle
- the value of alternating current that gives the same heating effect that the corresponding value of direct current does
An equivalent value allowing for accurate comparisons between alternating and direct current
Power can be calculated by using the appropriate rms values in the equations given previously

5. Effective Current Potential Difference Current Instantaneous values v
Maximum values
Vmax
Imax
rms values
Vrms=Vmax/√2 = 0.707*Vmax
Irms = Imax/√2 = 0.707*Imax

6. Effective Current Power = rms current squared * resistance
Power = one-half * maximum current squared * resistance
P = (Irms)2R = ½(Imax)2R
Ohm’s law still applies in ac circuits
Rms potential difference = rms current * resistance
Vrms = Irms*R

7. Effective Current
Sample problem: A generator with a maximum output emf of 205V is connected to a 115 resistor. Calculate the rms potential difference. Find the rms current through the resistor. Find the maximum ac current in the circuit.
Vmax = 205V R = 115
Vrms = ? Irms = ? Imax = ?
Vrms = .707*Vmax
Irms = Vrms / R
Irms = .707*Imax

8. Effective Current

9. Effective Current Resistance influences current in an ac circuit
The ac potential difference (ac voltage) measured in an electrical outlet is a rms emf with a value of 120V
Maximum emf value for an outlet is about 170V
Ammeters and voltmeters (and therefore multimeters) that measure alternating current are calibrated to measure rms values for current and emf (voltage)

10. Transformers
Transformer – a device that increases or decreases the emf of alternating current
In its simplest form, a transformer consists of two coils of wire wrapped around an iron core
The first coil, or primary or input coil, is connected to a voltage source
The second coil, or secondary or output coil, is connected to a resistor or other load
The relative number of times the coils are wrapped around the iron core determines what happens to the voltage
If the primary coil has more loops, the voltage decreases
Step-down transformer
If the secondary coil has more loops, the voltage increases
Step-up transformer

11. Transformers Transformer Equation
Induced emf in secondary coil = (number of turns in secondary coil) / (number of turns in primary coil) * applied emf in primary coil
ΔV2 =N2 / N1 * ΔV1
Can’t have something for nothing
Due to energy loss due to heating and radiation, so the output power will be less than the input power
Any increase in voltage must be offset by a proportional decrease in current
Real transformers have efficiency values of 90-99%
To minimize power lost by resistive heating (I2R loss) in transmission lines, electric lines have high emf values and low currents
Main lines have emf = V
Regional lines have emf = 20000V
Customer lines have emf = 120V

12. Transformers The ignition coil in a gasoline engine is a transformer
Changes 12 dc V into an emf of V to ignite and burn fuel when sparkplug fires
Crank angle sensor detects the crankshafts position to determine when the engine cylinder’s contents are at maximum compression