Exploring Inductors in Electro-Magnetic Circuits

[EvLer]

one more electro-magnetic question:
here's the set-up: two inductors, the A-B has a signal source hooked-up, C-D is open circuit.

->i1
A       C 
)    (    +
)    (    V2
)    (    -
B       D

i1 is given as a triangular wave, v2 as a step wave for:
0 < t < 0.5, i1 has negative slope below t-axis, v2=4;
0.5<t<1, i1 has positive slope below t-axis, v2 = -4;
1<t<1.5, i1 has positive slope above t-axis, v2 = 0

so, i clearly see that voltage is derivative of current and there is a negative sign involved, so the dots are placed diagonally?
If not, could you explain that as well?
Thanks in advance...

 

[EvLer]

solved

well... yeah, they should be on the opposite side, i think i got the idea...

 

[piercas]

I would like to first clarify that the dots in the circuit represent the polarity of the inductors, not the direction of current flow. The direction of current flow is determined by the direction of the voltage source and the polarity of the inductors.

In this set-up, the inductor A-B is connected to a signal source, while the inductor C-D is open circuit. This means that the current flowing through the inductor A-B will induce a voltage across the inductor C-D, but no current will flow through it.

Based on the given information, we can see that the current in i1 is given as a triangular wave, while the voltage in v2 is given as a step wave. This means that the voltage in v2 will change abruptly at specific time intervals, while the current in i1 will change gradually.

The relationship between voltage and current in an inductor is given by the equation V=Ldi/dt, where V is the voltage across the inductor, L is the inductance, and di/dt is the rate of change of current over time. This means that the voltage across the inductor is directly proportional to the rate of change of current.

In this set-up, we can see that when the current in i1 has a negative slope below the t-axis, the voltage in v2 is positive and has a value of 4. This means that the current is increasing at a constant rate, and the voltage across the inductor is also increasing at a constant rate. Similarly, when the current has a positive slope above the t-axis, the voltage in v2 is 0, indicating that the current is not changing and therefore there is no induced voltage across the inductor.

The negative sign in the equation V=Ldi/dt represents the direction of the induced voltage, which is opposite to the direction of the current. This is why the dots are placed diagonally in the circuit, to indicate the polarity of the inductors and the direction of the induced voltage.

I hope this explanation helps clarify your understanding of inductors in electro-magnetic circuits. If you have any further questions, please don't hesitate to ask. Thank you.