Exploring RLC Circuits: Lamp Brightness & Inductive Reactance

[dagg3r]

hi i got 2 questions here fairly confusing was wondering if i can get some help thanks

1. consider a series RLC circuit in which R is an incandescent Lamp C is some fixed capacitor and L is a variable inductance. The source is 240 V ac.
explain why the lamp glows brightly for some values for L and does not glow at all for other values

* not sure about this question but i am thinking along the lines that when capacitor discharge current + power source current = inductor current
when there is no current flow bulb won't glow can someone provide me with a better explanation thanks

2. an inductor is connected to a sinusoidal voltage with amplitude of 120V. A peak current of 3.0A appears in the inductor.

a)what is the maximum current if the frequency of the applid voltage is douled
b) what is the inductive reactance at each of the two frequencies?

* i know Vmax=120 i have the equations il=imaxsin(wt - pi/2)
and imax = Vmax / Xl whre Xl=wL
any ideas how to approach this question i tried using Imax=3 not working heh

 

[andrevdh]

1. The lamp will glow brightly when the current in the circuit is large, which will be the case when the total AC resistance of the circuit (the impedance) is small. The impedance of a series RCL circuit depends on the square of the difference between the reactances (AC resistances) of the capacitor and the inductor. If these two reactances is the same (a certain choice of L) the difference will be zero giving a small impedance and resulting large current in the series RCL circuit.

 

[quicknote]

1. In a series RLC circuit, when the inductance (L) is very low, the capacitor (C) and the resistor (R) dominate the circuit and the current flows mostly through them. This results in a small voltage drop across the inductor and a large voltage drop across the resistor, causing the lamp to glow brightly. However, when the inductance is increased, the inductor starts to dominate the circuit and the current flows mostly through it. This results in a larger voltage drop across the inductor and a smaller voltage drop across the resistor, causing the lamp to not glow at all. This is because the inductor opposes the change in current and resists the flow of current, causing the voltage drop across it to increase. This phenomenon is known as inductive reactance.

2. a) Doubling the frequency of the applied voltage results in a doubling of the current in the inductor, as seen from the equation Imax = Vmax / Xl. Therefore, the maximum current in the inductor will be 6.0A.

b) The inductive reactance (Xl) can be calculated using the equation Xl = wL, where w is the angular frequency (2*pi*f) and L is the inductance. At the original frequency, Xl = wL = (2*pi*f)*(L) = (2*pi*60)*(L) = 120L. At double the frequency, Xl = wL = (2*pi*2*60)*(L) = 240L. Therefore, the inductive reactance at the original frequency is 120L and at double the frequency it is 240L.