A resistor (R3000.0 ohms), a capacitor (C 0.400 micro F) and an inductor (L 5.00 H) are connected in series across a 440.0 Hz AC source for which change in V maximum 125 V. a) find the impedance of the circuit.b) find the maximum current delivered by the source.c) find the phase angle between the current and the voltage.d) Write a sentence describing the relationship between the current and the voltage in the circuit.e) find the maximum voltage across the resistor.f) find the maximum voltage across the capaitor.g) find the mazimum voltage across the inductor.h) find the resonat frequency of the cirsuit.i) find the rms current in the circuit at resonance.j) find the average power delivered to the circuit. Does anyone know how to do any of these or can tell me what formulas to use and how to use them i would really appreciate it!! Thank u!!
The formulae aren't that hard.? They're especially easy in a series circuit. First, we need to talk about omega (ω).? Omega is the angular frequency of a sinusoidal waveform, and it's equal to 2πf where f is the frequency in Hertz.? This allows you to express e.g. the applied voltage as 125 sin (ωt). Next, impedance.? Impedance can either be resistance (in phase with the current) or reactance (90° out of phase with the current).? Reactances are measured in imaginary ohms (yes, imaginary numbers!).? The convention is to represent √-1 as the letter j. The reactance of a perfect inductor is jωL The reactance of a perfect capacitor is 1/(jωC) Note that 1/j -j, so capacitive reactance is the opposite of inductive reactance. Now, to get the reactance of your series circuit you just calculate the reactances of the parts and add them all up.? Add the resistor, the inductor and the capacitor like this: Z 3000Ω + 880πj*5H + 1/(880πj*0.4μF) or, after noting that 1/j -j, Z 3000Ω + 880πj*5H - j/(880π*0.4μF) This will give you a complex number for Z, in ohms.?That's (a) The maximum current is the maximum voltage divided by the magnitude of Z.? That's (b). The phase angle is the angle of Z relative to the real axis, where inductive reactance (positive j) is lagging phase and capacitive reactance (negative j) is leading phase.? That's (c). That should get you going.
