Formulas for the alternating current and voltage

In summary, the formulas for voltage and current are v=v0cos(wt) and i=i0cos(wt). However, when searching for the answers online, the formulas v=v0sin(wt) and i=i0sin(wt) are also shown, but they are essentially the same with a phase difference of π/2. This phase difference can be calculated using trigonometry.
  • #1
wolly
49
2
Hi,I have found in my textbook the formulas for both current and voltage and I have no idea if they are right or wrong. Can someone help me with these formulas?
v=v0cos(wt)
i=i0cos(wt)
Is this correct? In google when I search for the answers I get something else:
v=v0sin(wt)
i=i0sin(wt)
 
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  • #2
They are same sinusoidal function with only difference of phase. 
Fot t=0
The former v=v0 i=i0
The latter v=0 i=0
 
  • #3
Yes if you know abit of trigonometry it is $$\cos(\omega t)=\sin(\omega t+\frac{\pi}{2})=\sin(\omega(t+t_0))$$ where ##t_0=\frac{\pi}{2\omega}## the phase difference in seconds.
 

FAQ: Formulas for the alternating current and voltage

What is an alternating current (AC)?

An alternating current is an electrical current that changes direction periodically. It is commonly used in household and industrial electrical systems.

What is the formula for calculating the frequency of an AC circuit?

The formula for calculating the frequency of an AC circuit is f = 1/T, where f is the frequency in Hertz (Hz) and T is the period in seconds.

How do you calculate the peak voltage of an AC circuit?

The peak voltage of an AC circuit can be calculated by multiplying the peak current by the impedance of the circuit. The formula is V = I*Z, where V is the peak voltage in volts, I is the peak current in amps, and Z is the impedance in ohms.

What is the relationship between AC voltage and current?

In an AC circuit, the voltage and current are not constant and change over time. However, the relationship between them can be described by Ohm's law, which states that V = I*R, where V is the voltage, I is the current, and R is the resistance.

How do you calculate the power in an AC circuit?

The power in an AC circuit can be calculated by multiplying the voltage by the current and the power factor. The formula is P = V*I*pf, where P is the power in watts, V is the voltage in volts, I is the current in amps, and pf is the power factor.

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