Alternating Current and RMS Derivation Whiteboards

Alternating Current Concept 0 V = V o sin(2  ft) I = I o sin(2  ft) V o = Peak V I o = Peak I Demo – oscilloscope - what is our V o ???

Alternating Current P = I 2 R = V 2 /R Average Power = 1 / 2 I o 2 R = 1 / 2 V o 2 /R What Is “effective” I and V? I rms = I o  2 V rms = V o  2 R Vac ~ rms = root mean square V rms and I rms is default - meters If people mean “peak”, they will say “peak” P = I rms V rms (= 1 / 2 I o V o ) What is our rms on the ‘scope?

Alternating Current Example - A ohm resistor has a peak voltage of Volts across it. What is the rms voltage across it, and what is the peak and rms current through it, and the power and peak power that it dissipates. I rms = I o V rms = V o  2  2 P = IV = V 2 /R = I 2 R (I and V must be rms) R = V/I R = ohms, V o = V V rms = V I o = (R = V o /I o ) I rms = A P = 1587 W (IV - use rms) P o = 3174 W (IV - use peak)

Whiteboards rms 11 | 2 | 3 | 4 | 5 |

What is the rms voltage if the peak voltage is 340 V? I rms = I o V rms = V o  2  V Given: V rms = V o  2 V o = 340 V V rms = ?? V rms = = 240 V (Europe) W

A circuit has an rms current of 1.45 A. What is the peak current? I rms = I o V rms = V o  2  A Given: I rms = I o  2 I o = ?? I rms = ?? I o = = 2.05 A W

What’s the rms voltage here? I rms = I o V rms = V o  2  2 11 V Given: V rms = V o  2 V o = 16 V V rms = ?? V rms = 11.3 = 11 V W +16 V -16 V

What is the peak voltage if the rms voltage is 12 V? I rms = I o V rms = V o  2  2 17 V Given: V rms = V o  2 V o = ?? V rms = 12 V V o = = 17 V W

An 60.0 V alternating current is attached to a device that draws 3.5 amps. What is the power used? I rms = I o V rms = V o  2  2 P = IV = V 2 /R = I 2 R (I and V must be rms) 210 W Given: V rms = V o  2 P = IV I rms = 3.5 A (if they don’t say peak…..) V rms = 60.0 P = ?? P = 210 W W

An alternating current with a peak voltage of 18.5 V is connected to a 27.5 ohm resistor. What power is dissipated? I rms = I o V rms = V o  2  2 P = IV = V 2 /R = I 2 R (I and V must be rms) 6.22 W Given: V rms = V o  2 P = V 2 /R V o = 18.5 V rms = ?? R = 27.5 ohms P = ?? V rms = V, P = = 6.22 W W

A 40. Watt light is connected to a 120 Volt source. What is the peak current through the light bulb, its resistance, and what is the peak power that it dissipates? I rms = I o V rms = V o  2  2 P = IV = V 2 /R = I 2 R (I and V must be rms).47 A, 360 ohms, 80. W Given: I rms = I o V rms = V o  2  2 P = V 2 /R I o = ?? V rms = 120 V R = ?? P = 40. W P o = ?? I rms =.333 A, I o =.4714 A, R = 360 ohms, P o = 80. W W

A ohm heating element is dissipating 1530 W of power. What are the peak current and peak voltage through and across the element? (find rms…) What is the peak power? I rms = I o V rms = V o  2  2 P = IV = V 2 /R = I 2 R (I and V must be rms) 5.5 A, 554 V, 3060 W Given: I rms = I o V rms = V o  2  2 P = V 2 /R = I 2 R V o = ?? I o = ?? R = ohms P = 1530 W V rms = V, V o = 553.7, I rms = A, I o = A, P o = 3060 W W