answer
The universal relay torque equation isT=k1I2+k2V2+k3VIcos(a-e)+K
where
T= maximum torque
V= R.m.S magnitude of voltage
I= R.M.S magnitude of current
The spring torque will be K .
a= angle between V&I
e=max torque angle
Because an inductor resists a change in current. The equation of an inductor is ...di/dt = V/L... meaning that the rate of change of current is proportional to voltage and inversely proportional to inductance. Solve the differential equation in a sinusoidal forcing function and you get inductive reactance being ...XL = 2 pi f L
Work it out for yourself. The equation is: Z = E/I, where Z is the impedance, E is the supply voltage, and I is the load current.
While it is true that an inductor opposes the flow of an alternating current, it does not necessarily 'block it'. The quantity that opposes the flow of an AC current is the inductor's inductive reactance, expressed in ohms. Inductive reactance is proportional to the frequency of the supply voltage and, at 50 or 60 Hz, the reactance of a transformer's winding is relatively low (although very much higher than its resistance) and, while this acts to limit the amount of current flow, it certainly doesn't act to block that flow.
Do it yourself. The equation is Xc = 1 / (2 pi f C). Be sure to convert microfarads to farards, first!
The equation of an inductor is ...di/dt = L / V... which means that the rate of change of current is proportional to voltage and inversely proportional to inductance.Set this up in a sinusoidal forcing circuit and solve the differential equation, or use phasors, and you get ...XL = 2 pi f L... which means that inductive reactance is proportional to both frequency and inductance by the factor of 2 pi.I have not included the derivation, because I don't know how to do it, and it does not seem necessary. If someone wants to provide one, please feel free to refine the answer.
Because an inductor resists a change in current. The equation of an inductor is ...di/dt = V/L... meaning that the rate of change of current is proportional to voltage and inversely proportional to inductance. Solve the differential equation in a sinusoidal forcing function and you get inductive reactance being ...XL = 2 pi f L
Xc(capacitive reactance) = 1/(2piFC)XL(inductive reactance) = 2piFLWhere pi=3.14etc.,F=frequency and C and L are capacitance and inductance.Please pardon lack of proper symbology.
Work it out for yourself. The equation is: Z = E/I, where Z is the impedance, E is the supply voltage, and I is the load current.
it depends on capacitance and frequency, both inversely. Check your AC circuits textbook for the exact equation.
The isolation transformer provides a electrical mean to separate the source and load. Also, The isolation transformer will protect against surges and spikes as the primary winding due to it's magnetic property will impose more resistance (reactance) to higher frequencies such as spikes and such. where Xl is the impedance (resistance) of the primary winding. In this equation, one can see that higher frequencies increast the impedance of the coil proportionally to the rate of frequency.
Set 0=(denominator of the System Transfer Function), this is the Characteristic Equation of that system. This equation is used to determine the stability of a system and to determine how a controller should be designed to stabilize a system.
Q=d
Simple addition, but it must be done with complex numbers.
The Universal Law of Gravitation is a force equation, therefore it should have units of Newtons.
Qn =JQ'+K'Q
An inductor blocks AC while allowing DC because it resists a change in current. The equation of an inductor is ...di/dt = V/L... meaning that the rate of change of current is proportional to voltage and inversely proportional to inductance.If you apply DC across an inductor, it will stabilize to some current flow based on the maximum current available from the current / voltage source. In this mode, the inductor presents very low resistance, so it can be said that it allows DC to pass.If, however, you apply AC across an inductor, you need to consider its inductive reactance by integrating the above equation in terms of the circuit conditions. The equation for inductive reactance is ...XL = 2 pi F L... meaning that the inductive reactance is proportional to the frequency and to the inductance.Thus, the higher the frequency, the higher the reactance. Since reactance is a phasor measure of resistance, it can be thus said that an inductor will block AC.
The equation is F = GmM/r2 whereF is the force of gravity, G is the universal gravitational constant, m and M are the two masses, and r is the distance between the masses.