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. $$X_L\propto f$$