__Instantaneous Power Calculator:__

__Instantaneous Power Calculator:__

Enter the values of peak voltage, V_{p(V)}, peak current, I_{p(A)}, angular frequency, ω_{(rad/s)}, time, t_{(s)}, phase angle of the voltage, av_{(rad)} and phase angle of the current, ai_{(rad)} to determine the value of Instantaneous Power, P_{t(W)}.

__Instantaneous Power Formula:__

__Instantaneous Power Formula:__

Instantaneous power is the power consumed by an electrical device at a specific moment in time.

It is measured in watts (W) and represents the product of the instantaneous voltage and the instantaneous current at that moment.

In AC circuits, both voltage and current vary sinusoidally over time. Therefore, instantaneous power also varies and can be positive or negative, indicating the direction of power flow.

Instantaneous power is crucial for understanding the power behaviour in dynamic systems, such as in power electronics and AC machinery.

**Peak voltage, V _{p(V)} **represents the peak voltage of the AC source, which is the maximum voltage it can supply (measured in volts).

**Peak current, I _{p(A) }**represents the peak current of the AC source, which is the maximum current it can deliver (measured in amperes).

Angular frequency of the AC source, measured in radians per second. It essentially determines how quickly the voltage and current waveforms change direction.

Instantaneous Power, P_{t(W)} in watts is equal to the product of the peak voltage, V_{p(V)} in volts, peak current, I_{p(A)} in amperes, the cosine of the sum of the angular frequency, ω_{(rad/s)} in radians per second multiplied by time, t_{(s)} in seconds and the phase angle of the voltage, av_{(rad)} in radians and the cosine of the sum of the angular frequency, ω_{(rad/s) }multiplied by time, t_{(s)} and the phase angle of the current, ai_{(rad)} in radians.

Instantaneous Power, P_{t(W)} = V_{p(V) }* I_{p(A)} * cos(ω_{(rad/s)} * t_{(s)} + av_{(rad)}) * cos(ω_{(rad/s)} * t_{(s)} + ai_{(rad)})

P_{t(W)} = instantaneous power in watts, W.

V_{p(V)} = peak voltage in volts, V.

I_{p(A)} = peak current in amperes, A.

ω_{(rad/s)} = angular frequency in radians per second, rad/s.

t_{(s)} = time in seconds, s.

av_{(rad)} = phase angle of voltage in radians, rad.

ai_{(rad)} = phase angle of current in radians, rad.

__Instantaneous Power Calculation:__

__Instantaneous Power Calculation:__

- A circuit has a peak voltage of 120 volts (V), a peak current of 5 amperes, an angular frequency of 100 radians per second, and both voltage and current have a phase angle of 0 radians. Calculate the instantaneous power at time 0.01 seconds.

Given: V_{p(V)} = 120V, I_{p(A)} = 5A, ω_{(rad/s)} = 100rad/s, t_{(s)} = 0.01s, av_{(rad)} = 0rad,

ai_{(rad)} = 0rad.

Instantaneous Power, P_{t(W)} = V_{p(V) }* I_{p(A)} * cos(ω_{(rad/s)} * t_{(s)} + av_{(rad)}) * cos(ω_{(rad/s)} * t_{(s)} + ai_{(rad)})

P_{t(W)} = 120 * 5 * cos (100 * 0.01 + 0) * cos (100 * 0.01 + 0)

P_{t(W)} = 600 * cos (1) * cos (1)

P_{t(W)} = 600 * 0.5403 * 0.5403

P_{t(W)} = 600 * 0.2919

P_{t(W)} = 175.14W.

- A circuit has a peak current of 10 amperes, an angular frequency of 50 radians per second and the phase angle of the voltage is 0.5 radians. The instantaneous power at time 0.02seconds is 200 watts. The phase angle of the current is -0.5 radians. Calculate the peak voltage.

Given: ai_{(rad)} = -0.5rad, I_{p(A)} = 10A, ω_{(rad/s)} = 50rad/s, t_{(s)} = 0.02s, av_{(rad)} = 0.5rad,

P_{t(W)} = 200W**.**

Instantaneous Power, P_{t(W)} = V_{p(V) }* I_{p(A)} * cos(ω_{(rad/s)} * t_{(s)} + av_{(rad)}) * cos(ω_{(rad/s)} * t_{(s)} + ai_{(rad)})

V_{p(V)} = P_{t(W)} / I_{p(A)} * cos(ω_{(rad/s)} * t_{(s)} + av_{(rad)}) * cos(ω_{(rad/s)} * t_{(s)} + ai_{(rad)})

V_{p(V)} = 200 / 10 * cos(50 * 0.02 + 0.5) * cos(50 * 0.02 – 0.5)

V_{p(V)} = 200 / 10 * cos(1.5) * cos(0.5)

V_{p(V)} = 200 / 10 * 0.0707 * 0.8776

V_{p(V)} = 200 / 0.621

V_{p(V)} = 322.06V.

__Instantaneous Power in AC Circuits:__

__Instantaneous Power in AC Circuits:__