AC circuits

Question 1

What is a capacitor?

Answer 1

A capacitor is formed from two conducting plates separated by a thin layer called dielectric.

Question 2

How does a capacitor work?

Answer 2

If a current (i) flows, positive charge (q) accumulates on the upper plate, while a balancing negative charge is present on the lower plate.

Question 3

What is the formula for potential energy difference (voltage) in a capacitor?

Answer 3

v = d / (Aε) * q

Question 4

What does capacitance measure?

Answer 4

Capacitance is the ability of the capacitor to store electric charges.

Question 5

What is the relationship between capacitance (C), charge (q), and voltage (v)?

Answer 5

C = q / v

Question 6

What is the unit of capacitance?

Answer 6

Farad (F)

Question 7

What is the formula for capacitance of a parallel-plate capacitor?

Answer 7

C = (ε0εrA) / d

Question 8

What do ε0 and εr represent in the capacitance formula?

Answer 8

ε0 is the absolute permittivity of free space, and εr is the relative permittivity of the dielectric material.

Question 9

What is the capacitance of a multi-plate capacitor with uniform dielectric?

Answer 9

C = (ε0εrA) / d * (n - 1)

Question 10

What is the formula for capacitance of a multi-plate capacitor with different dielectrics?

Answer 10

C = (d1 / (εr1 + εr2 + εr3)) * (ε0A / d2)

Question 11

What is the characteristic of capacitors connected in series?

Answer 11

The total charge (Qt) is equal across all capacitors: Qt = Q1 = Q2 = … = Qn.

Question 12

What is the voltage relation for capacitors in series?

Answer 12

The total voltage (Vt) is the sum of individual voltages: Vt = V1 + V2 + … + Vn.

Question 13

What is the capacitance relation for capacitors in series?

Answer 13

1 / Ct = 1 / C1 + 1 / C2 + … + 1 / Cn.

Question 14

What is the characteristic of capacitors connected in parallel?

Answer 14

The total voltage (Vt) is equal across all capacitors: Vt = V1 = V2 = … = Vn.

Question 15

What is the capacitance relation for capacitors in parallel?

Answer 15

Ct = C1 + C2 + … + Cn.

Question 16

What is an inductor?

Answer 16

An inductor is a passive electrical component that stores energy in its magnetic field.

Question 17

What is the current relation for inductors in series?

Answer 17

The current (i) is the same through all inductors: di/dt = di1/dt = di2/dt = … = din/dt.

Question 18

What is the voltage relation for inductors in series?

Answer 18

Vt = V1 + V2 + … + Vn.

Question 19

What is the inductance relation for inductors in series?

Answer 19

Lt = L1 + L2 + … + Ln.

Question 20

What is the current relation for inductors in parallel?

Answer 20

di/dt = di1/dt + di2/dt + … + din/dt.

Question 21

What is the voltage relation for inductors in parallel?

Answer 21

Vt = V1 = V2 = … = Vn.

Question 22

What is the inductance relation for inductors in parallel?

Answer 22

1 / Lt = 1 / L1 + 1 / L2 + … + 1 / Ln.

Question 23

What is reactance in AC circuits?

Answer 23

Reactance is the non-resistive component of impedance, arising from inductance or capacitance.

Question 24

What is impedance in AC circuits?

Answer 24

Impedance is the effective resistance of an electric circuit to alternating current, combining ohmic resistance and reactance.

Question 25

In a capacitor, current leads voltage by how many degrees?

Answer 25

90 degrees.

Question 26

In an inductor, voltage leads current by how many degrees?

Answer 26

90 degrees.

Question 27

What does the term 'in-phase' mean in AC circuits?

Answer 27

Voltage and current reach their zero, peak, and valley points at the same time.

Question 28

What is Euler's identity?

Answer 28

e^(j(ωt + φ)) = cos(ωt + φ) + j sin(ωt + φ)

Question 29

What does the phase angle (φ) represent?

Answer 29

The phase angle in degrees or radians.

Question 30

What is the formula for angular frequency (ω)?

Answer 30

ω = 2πf

Question 31

What is the relationship between frequency (f) and period (T)?

Answer 31

T = 1/f

Question 32

What is the rms value of a current?

Answer 32

The effective value of an alternating current.

Question 33

What happens when AC voltage is applied across pure resistance?

Answer 33

It draws a current that is in-phase with the AC voltage.

Question 34

What happens when AC voltage is applied across pure inductance?

Answer 34

It draws a current that lags the AC voltage by 90 degrees.

Question 35

What is the current behavior in a pure inductance when AC voltage is applied?

Answer 35

The current lags the AC voltage by an angle of 90°.

Question 36

In the formula ( X_L = 2pi f L ), what does each symbol represent?

Answer 36

* ( X_L ) = inductive reactance, ohms * ( f ) = frequency, Hertz (Hz) * ( L ) = inductance, Henry (H)

Question 37

What occurs when an AC voltage is applied across pure capacitance?

Answer 37

The current leads the AC voltage by an angle of 90°.

Question 38

What is the formula for capacitive reactance?

Answer 38

The formula is ( X_C = rac{1}{2pi f C} ).

Question 39

In a series R-L circuit, how does the current behave with respect to the AC voltage?

Answer 39

The current lags the AC voltage with an acute angle Ɵ.

Question 40

What is the formula for total impedance in a series R-L circuit?

Answer 40

The formula is ( Z = sqrt{R^2 + X_L^2} ).

Question 41

What happens in a series R-C circuit when an AC voltage is applied?

Answer 41

The current leads the AC voltage with an acute angle Ɵ.

Question 42

What is the behavior of current in a series L-C circuit?

Answer 42

The current can either lag or lead with the AC voltage by an angle of 90°.

Question 43

In a series R-L-C circuit, how does the current behave?

Answer 43

The current can either lag, lead, or be in-phase with the AC voltage.

Question 44

What is the formula for total impedance in a series R-L-C circuit?

Answer 44

The formula is ( Z = sqrt{R^2 + (X_L - X_C)^2} ).

Question 45

What is the relationship for total impedance in a series circuit?

Answer 45

The total impedance ( Z_t = Z_1 + Z_2 + ... + Z_n ).

Question 46

What is the formula for total impedance in a parallel circuit?

Answer 46

The formula is ( rac{1}{Z_t} = rac{1}{Z_1} + rac{1}{Z_2} + ... + rac{1}{Z_n} ).

Question 47

What is the basis of nodal analysis in AC circuits?

Answer 47

The basis is Kirchhoff’s current law (KCL).

Question 48

What forms the basis of mesh analysis?

Answer 48

Kirchhoff’s voltage law (KVL) forms the basis.

Question 49

Fill in the blank: In a series R-C circuit, the total impedance is given by ( Z = sqrt{R^2 + ______^2} ).

Answer 49

X_C

Question 50

True or False: In a series L-C circuit, the current is always lagging.

Answer 50

False

Question 51

What does KCL stand for?

Answer 51

Kirchhoff's Current Law.

Question 52

What does KVL stand for?

Answer 52

Kirchhoff's Voltage Law.

Question 53

What angle does the current lag in a series R-L circuit?

Answer 53

The current lags with an acute angle Ɵ.

Question 54

What angle does the current lead in a series R-C circuit?

Answer 54

The current leads with an acute angle Ɵ.

Question 55

What is the impedance in a series circuit with an inductive reactance of 8 Ω and a capacitive reactance of 18 Ω connected in parallel?

Answer 55

The total impedance is 16.62 Ω.

Question 56

What is the impedance of a circuit with resistance R and inductive reactance X_L?

Answer 56

The impedance ( Z = sqrt{R^2 + X_L^2} ).

Question 57

What is the value of inductance that causes a current of 2 A lagging in a series L-C circuit?

Answer 57

The value of inductance must be calculated based on the circuit parameters.