For a circuit containing a coil, the impedance is given by XL=L, and for a circu

Question

For a circuit containing a coil, the impedance is given by XL=L, and for a circuit containing a capacitor, the impedance is given by XC=1C , where L in the inductance of the coil and C is the capacitance of the capacitor. 1. Let’s consider an AC circuit containing a coil.

a) How does the impedance for this circuit change if the inductance is increased?

b) How does the impedance for this circuit change if the frequency of oscillation of the voltage is increased?

c) List several ways (if there is more than one) to increase the current in an AC circuit containing a coil.

2. Now Let’s consider an AC circuit containing a capacitor.

a) How does the impedance for this circuit change if the capacitance is increased?

b) How does the impedance for this circuit change if the frequency of oscillation of the voltage is increased?

c) List several ways (if there is more than one) to increase the current in an AC circuit containing a capacitor.

3. For fun, let’s consider an AC circuit containing a resistor.

a) How does the impedance for this circuit change if the resistance is increased?

b) How does the impedance for this circuit change if the frequency of oscillation of the voltage is increased?

c) List several ways (if there is more than one) to increase the current in an AC circuit containing a capacitor.

d) What is the formula for the impedance of this circuit, XR?

Explanation / Answer

(1) for the first case when circuit containing the coil

part(a)

given that

impedence XL = wL

from this relation we can see that

impedence directly propotional to the inductance so when we increased the inductance impedence should be increasede.

part(b)

we know that

f = 1/2*pi*sqrt(L*C)

from above relation it is clear that frequency is inversely propotional to inductance so when we increase the frequency inductance should be decrease .

and when inductance decreases impedence should be decreases.

part(c)

we can increase the current :

by increasing the AC voltage,

by decreasing the inductance ,

by decreasing the frequency of oscillation .

(2) for the second case when circuit containing capacitor

part(a)

given that

XC = 1/(w*C)

from this relation we can see that

impedence inversely propotional to the capacitance so when we increased the capacitance impedence should be decrease

part(b).

we know that

f = 1/2*pi*sqrt(L*C)

from above relation it is clear that frequency is inversely propotional to capacitance so when we increase the frequency capacitance should be decrease .

and when capacitance decreases impedence should be increases.

part(c)

we can increase the current :

by increasing the AC voltage,

by increasing the capacitance ,

by decreasing the frequency of oscillation .

(3) for the case when circuit containing resistance

part(a)

impedence XR = R

when resistance increassed from above relation impedence should be increased.

part(b)

we know that

f = 1/2*pi*sqrt(L*C)

from above relation it is clear that frequency does not affect the resistance so when frequency increases impedence remains same.

part(c)

we can increase the current :

by increasing the AC voltage,

by decreasing the resistance ,

part(d)

impedence

XR = R

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