- #1
CosmicC
how we can mathematically prove that in a purely inductive circuit current lags behind voltage by a phase angle of π/2?
Welcome to the PF.CosmicC said:how we can mathematically prove that in a purely inductive circuit current lags behind voltage by a phase angle of π/2?
Yes Sir I am.berkeman said:Welcome to the PF.
1) Is this a question for your homework or schoolwork?
2) << EDIT -- I removed this point since it might not be accurate >>.
3) Are you familiar with the differential equation defining the voltage across an inductor v(t) as a function of the inductance and the derivative of the current i(t) through the inductor?
First you have to define voltage as some math function.CosmicC said:how we can mathematically prove that in a purely inductive circuit current lags behind voltage by a phase angle of π/2?
So you're aware e = L X di/dtCosmicC said:Yes Sir I am.
Yes Now i get it. And even both the curves has difference of ninety degrees. Thanks a lot.jim hardy said:First you have to define voltage as some math function.
Your question infers sine function but doesn't say that's what it is. Sine is a mathematical oddity in that its derivative and integral have its same shape .
so we use them almost interchangeably
Once you realize that it's trivial So you're aware e = L X di/dt
∫e dt = L X ∫di ;
i = 1/L X ∫e dt
if e = sin wt , i = 1/L X ∫sin(wt) = -1/ωL X cos(wt) if i didnt miss a sign someplace
and cosine is just sine shifted ninety degrees ..
Draw it out ?
Solved. Thanks a lot. :)BvU said:So we can mark this one as solved ? Or is there a remaining question ?
A purely inductive circuit is a type of electrical circuit that contains only inductors and no other components, such as resistors or capacitors. This means that the circuit is purely reactive and does not dissipate any power.
Current lag refers to the delay between the voltage and current in a purely inductive circuit. This delay is caused by the inductor's ability to store energy in its magnetic field, which results in the current being out of phase with the voltage.
A mathematical proof is needed to fully understand and explain the phenomenon of current lag in a purely inductive circuit. It provides a rigorous and logical explanation for the relationship between voltage, current, and time in this type of circuit.
The proof for current lag in a purely inductive circuit involves using the principles of calculus and complex numbers to analyze the circuit's behavior. The proof shows that the current lags the voltage by 90 degrees in a purely inductive circuit.
Understanding current lag in a purely inductive circuit is important in various practical applications, such as power factor correction and designing efficient electrical systems. It also allows engineers to accurately predict and control the behavior of these circuits in different situations.