Resistors, Capcitors And Inductors

Question 1

What is the relationship between v and i in a resistive circuit

Answer 1

V and I are in phase

Question 2

convert v and i time representations in a resistive circuit to a phasors representation

Answer 2

V = Vm sin(ωt) —> V = Vm / sqrt(2) < 0

I = Vm/R sin(ωt) —> V = Vm / sqrt(2)R < 0

Question 3

relationship between v and i in an inductive circuit

Answer 3

I lags V by 90°

Question 4

Flux created by a coil

Answer 4

φ = μ Ni A / l

permeability of free space (μ)
number of turns (Ni)
coil area (A)
coil length (l)

Question 5

Faraday’s Law

Answer 5

voltage induced in a coil is proportional to the rate of change of flux linkage

v = d/dt (Nφ)

Question 6

inductance (L) in Henry’s (H)

Answer 6

L = flux * N = μ N^2 A / l

Question 7

convert v and i time representations in a resistive circuit to a phasors representation

Answer 7

v = Vm sin(ωt +0) —> V = Vm / sqrt(2) < 0

i = Vm/ωL sin(ωt - π/2) —> I = Vm / sqrt(2) ω L < -90°

Question 8

What is reactance in an AC circuit?

Answer 8

Reactance (X) is the opposition that inductors and capacitors provide to alternating current (AC). It results from the ability of these components to resist changes in current and voltage. For inductors, reactance increases with frequency, while for capacitors, it decreases with frequency.

Question 9

What is the difference between inductive reactance and capacitive reactance?

Answer 9

• Inductive Reactance (X_L): Opposition to AC due to an inductor. X_L = ωL, where ω = 2π f is the angular frequency, and L is the inductance. Reactance increases with frequency.
• Capacitive Reactance (X_C): Opposition to AC due to a capacitor. The formula is X_C = 1 / ωC, where C is the capacitance. Reactance decreases with frequency.

Question 10

What is impedance in an AC circuit?

Answer 10

Impedance (Z) is the total opposition to current in an AC circuit, combining both resistance (R) and reactance (X). It is a complex quantity, meaning it has both magnitude and phase. The impedance is calculated using the formula:

Z = sqrt(R^2 + X^2)

where X is the total reactance (X_L - X_C).

Question 11

How does impedance differ from resistance in DC and AC circuits?

Answer 11

• In a DC circuit, impedance is simply equal to resistance (Z = R) because there is no reactance.
• In an AC circuit, impedance is a complex quantity that includes both resistance and reactance. The magnitude of impedance gives the total opposition to current, while the phase angle gives the phase difference between voltage and current.

Question 12

How is impedance represented in phasor form?

Answer 12

Impedance can be represented as a complex number in phasor form, with both magnitude and phase. For an AC circuit with an inductor, the impedance is Z_L = jωL, where j is the imaginary unit and ωL is the inductive reactance.

Question 13

inductive reactance

Answer 13

The inductive reactance is given by the formula:

X_L = ωL

where ω = 2π f is the angular frequency and L is the inductance of the coil. The inductive reactance increases with frequency because the inductor resists changes in current more at higher frequencies.

Question 14

How is the impedance of an inductor expressed in terms of reactance?

Answer 14

A: The impedance of an inductor is represented as:

Z_L = jωL

where ω is the angular frequency and L is the inductance. The term j indicates a 90° phase shift, meaning that the current lags the voltage by 90° in an inductive circuit.

Question 15

How is the impedance of an inductor expressed in terms of reactance?

Answer 15

A: The impedance of an inductor is represented as:

Z_L = jωL

where ω is the angular frequency and L is the inductance. The term j indicates a 90° phase shift, meaning that the current lags the voltage by 90° in an inductive circuit.

Question 16

How is Ohm’s law applied to AC circuits with inductive or capacitive reactance?

Answer 16

In AC circuits, Ohm’s law is applied using impedances instead of resistances. The law states:

V = I Z

where V is the voltage, I is the current, and Z is the impedance. For inductive circuits, use Z_L and for capacitive circuits, use Z_C

Question 17

How does the total impedance behave in AC circuits with resistors, inductors, and capacitors in series?

Answer 17

The total impedance Z_total in a series AC circuit is the sum of the individual impedances:

Z_total = Z_R + Z_L + Z_C

The total impedance accounts for both the resistive and reactive effects in the circuit.

Question 18

How is the impedance of an capacitor expressed in terms of reactance?

Answer 18

Z_C = 1 / jωC

Question 19

Why is impedance matching important?

Answer 19

Maximum Power Transfer: Ensures the load receives the most power from the source.
Minimizes Reflections: Prevents signal reflections in high-frequency systems, improving efficiency and clarity.
Enhances Signal Quality: Reduces distortion and loss in data transmission.
Prevents Damage: Avoids excess power reflecting back, protecting components like amplifiers.