Alternating Current [INCOMPLETE]

In Progress

What are the two conditions required for a current to be an alternating current?

1. Amplitude is constant

2. Alternate half cycle is positive and negative

If I=I_0\sin(\omega t ) then what is the value of the x axis at this point?

\dfrac{\pi}{\omega}

What is average emf for 1 time period?

0

What is the formula for average emf in half a time period? (there are 3)

\varepsilon_{\text{avg}}=\dfrac{\text{area under}\ \varepsilon\text{-}t\ \text{curve}}{\Delta t}=\dfrac{\int \varepsilon\ dt}{\int dt}=\dfrac{2\varepsilon_0}{\pi}  

where \varepsilon_0 is the peak voltage.

What is the formula for average current in half a time period? (there are 3)

I_{\text{avg}}=\dfrac{\text{area under}\ I\text{-}t\ \text{curve}}{\Delta t}=\dfrac{\int I\ dt}{\int dt}=\dfrac{2I_0}{\pi}

where I_0 is the peak current.

What is the formula for rms value of current?

I_{rms}=\sqrt{<I²>}=\sqrt{\dfrac{\int I^2\ dt}{\int dt}}=\dfrac{I_0}{\sqrt{2}} (the last one is for sinusodial current) 

for two currents:

I_{rms}=\sqrt{<(I_1+I_2)²>}=\dfrac{\sqrt{\text{sum of squares of peaks}}}{\sqrt{2}}

What is the formula for peak value of current when there are multiple currents for which you know the peaks?

I_{\text{peak}}=\sqrt{\text{sum of squares of peaks}}

What is the formula for rms value of voltage?

V_{rms}=\sqrt{<V²>}=\sqrt{\dfrac{\int V^2\ dt}{\int dt}}=\dfrac{V_0}{\sqrt{2}} last one is for sinusodial emf)

AC-measuring instruments always measure ____ (peak, rms) value of current/voltage. Why?

AC-measuring instruments always measure rms value of current/voltage, because they measure the heating effects of it.

In a purely resistive circuit, what is the phase difference between current and voltage? Which one leads the other?

0, neither leads.

In a purely inductive circuit, what is the phase difference between current and voltage? Which one leads the other?

phase difference is \frac{\pi}2 and voltage leads current.

In a purely capacitive circuit, what is the phase difference between current and voltage? Which one leads the other?

phase difference is \frac{\pi}2 and current leads voltage.

What is the formula for capacitive reactance?

X_C=\dfrac{1}{\omega C}

What is the formula for inductive reactance?

X_L=\omega L

What does the graph look like for \varepsilon,I by t in a purely resistive circuit?

What does the graph look like for \varepsilon,I by t in a purely inductive circuit?

What does the graph look like for \varepsilon,I by t in a purely capacitive circuit?

When AC flows through a circuit, what is the emf induced in an inductor? Explain why it is positive or negative sign.

\varepsilon=-L\dfrac{dI}{dt}

it is negative because the emf induced is in opposite polarity to the emf applied.

What is the unit of reactive inductance and reactive capacitance?

Ohm

Which of the following is true:

1. X_L\propto f

2. X_L \propto \dfrac{1}{f}

1. X_L\propto f