Question 1

The impedance (Z) of an RLC circuit with 15 $\Omega$ resistor, 7 $\Omega$ capacitive reactance, and 12 $\Omega$ inductive reactance is

Accepted Answer

The impedance (Z) of an RLC circuit is calculated using the formula $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $R$ is the resistance, $X_L$ is the inductive reactance, and $X_C$ is the capacitive reactance. Substituting the given values, $Z = \sqrt{15^2 + (12 - 7)^2} = \sqrt{225 + 25} = \sqrt{250} = 15.81 \Omega$, which is approximately 16 $\Omega$.

Question 2

A transformer has 90 turns on the primary coil and 175 turns on the secondary coil. If the input voltage is 120 VAC, the output voltage is

Accepted Answer

The output voltage can be calculated using the transformer equation: $V_{out} = V_{in} \times \frac{N_{secondary}}{N_{primary}}$, where $V_{in}$ is the input voltage, $N_{secondary}$ and $N_{primary}$ are the number of turns on the secondary and primary coils, respectively. Substituting the given values: $V_{out} = 120 \times \frac{175}{90} = 233.33$ VAC, which is approximately 230 VAC.

Question 3

A transformer has 90 turns on the primary coil and 175 turns on the secondary coil. If the AC input current is 5 A, the output current is

Accepted Answer

The transformer's output current can be calculated using the formula $I_2 = \frac{N_1}{N_2} \times I_1$, where $I_2$ is the output current, $N_1$ and $N_2$ are the number of turns on the primary and secondary coils, respectively, and $I_1$ is the input current. Substituting the given values: $I_2 = \frac{90}{175} \times 5 = 2.57$ A, which rounds to 2.6 A.

Question 4

In an ideal transformer, the physical quantity that is conserved from the input to the output is

Accepted Answer

In an ideal transformer, power is conserved from the input to the output. The power input at the primary coil is equal to the power output at the secondary coil, assuming no losses.

Question 5

In the transfer of electrical energy over power lines, it is desirable to minimize Joule heating. Therefore it is desirable to reduce the

Accepted Answer

Joule heating is directly proportional to the resistance of the conductor and the square of the current flowing through it, as described by the formula P = I^2R, where P is the power (heat generated), I is the current, and R is the resistance. Therefore, reducing both resistance and current can help minimize Joule heating. Reducing voltage is not directly related to minimizing Joule heating in this context, as higher voltage can actually be used to reduce current for a given power transmission, which in turn reduces Joule heating.

Question 6

In the transfer of electrical energy over power lines, it is desirable to minimize Joule heating by increasing the operating voltage. What prevents the energy company from stepping up the voltage to an extremely high level?

Accepted Answer

Corona discharge becomes a significant issue at extremely high voltages, leading to energy losses. It occurs when the electric field around a conductor is strong enough to ionize the air near it, causing energy to be dissipated.

Question 7

A particular transformer has a greater number of turns on the secondary winding than on the primary winding. This transformer is called

Accepted Answer

A transformer with more turns on the secondary winding than on the primary winding increases the voltage from the primary to the secondary, making it a step-up transformer.

Question 8

If the current is stepped up in a transformer, the

Accepted Answer

In a transformer, when the current is stepped up, the voltage is stepped down to conserve power, assuming ideal conditions with no losses. Therefore, the power remains constant.

Question 9

As the impedance in a simple series AC circuit gets larger, all of the following statements are valid except

Accepted Answer

In a simple series AC circuit, if the impedance increases, for a given AC voltage, the current through the circuit decreases according to Ohm's Law (V = IR), where V is voltage, I is current, and R (or Z in AC circuits, representing impedance) is resistance. Since power (P) in an electrical circuit is calculated as P = VI (or alternatively P = I^2R or P = V^2/R), if the current decreases while the voltage remains constant, the power delivered to the circuit also decreases. Therefore, statement D is incorrect because it suggests that power increases, which contradicts the relationship between power, voltage, and current in electrical circuits.

Question 10

At high frequencies, the reactances of an inductor and capacitor are

Accepted Answer

At high frequencies, the reactance of an inductor increases (making it large), while the reactance of a capacitor decreases (making it small).

Question 11

In a simple series RC circuit with a sinusoidal driving voltage, the phase relationship for a capacitor is that the

Accepted Answer

In a simple series RC circuit with a sinusoidal driving voltage, the current leads the voltage across the capacitor by 90°. This is because the capacitor's charging and discharging behavior causes the current to reach its maximum before the voltage does.

Question 12

In a simple series AC circuit, an explanation for the phase relationship between current and voltage for a capacitor is that the voltage across a capacitor is proportional to

Accepted Answer

In a capacitor, the voltage across it is proportional to the time integral of the current flowing through it. This relationship is described by the equation V = (1/C) ∫ i(t) dt, where V is the voltage, C is the capacitance, and i(t) is the current as a function of time. This integral relationship results in the voltage lagging the current by 90 degrees in phase in an AC circuit.

Question 13

For ideal elements, energy can be dissipated in

Accepted Answer

For ideal elements, energy is dissipated (i.e., converted into heat) only in a resistor. Capacitors and inductors store energy in their electric and magnetic fields, respectively, but do not dissipate it.

Question 14

The natural frequency for an LC circuit is

Accepted Answer

The natural frequency of an LC circuit is given by the formula $f = \frac{1}{2\pi\sqrt{LC}}$, which can be related to the angular frequency $\omega = \frac{1}{\sqrt{LC}}$, indicating option D, $(1/LC)^{1/2}$, is correct.

Question 15

We can check the answer to the previous question by remembering that the LC system is analogous to a mass-spring system whose natural frequency is (k/m) $1 / 2$ . The correct analogy is

Accepted Answer

The correct analogy between an LC circuit and a mass-spring system is that the capacitance (C) is inversely proportional to the spring constant (k), and the inductance (L) is directly proportional to the mass (m). This is because the natural frequency of an LC circuit is given by $1/\sqrt{LC}$, which is analogous to the natural frequency of a mass-spring system, $\sqrt{k/m}$.

Question 16

A possible clue to question 35 is that the electrical element that exhibits "inertia to the change of the current" is the

Accepted Answer

The electrical element that exhibits "inertia to the change of the current" is the inductor. This property is due to the magnetic field created around the inductor when current flows through it, resisting changes in the current.

Question 17

The term in an RLC circuit that has the units of time (seconds) is

Accepted Answer

The term in an RLC circuit that has the units of time (seconds) is L/R. This is because the unit of inductance (L) is henrys (H), which is defined as volts per second (V/s). The unit of resistance (R) is ohms (Ω), which is defined as volts per ampere (V/A). Therefore, the unit of L/R is (V/s)/(V/A) = s.

Question 18

If the resistance for a simple series RLC circuit is increased, the resonant frequency of that circuit (provided it still readily oscillates)

Accepted Answer

Increasing the resistance in a series RLC circuit decreases the resonant frequency.

Question 19

The quality factor ("Q") of a simple series RLC circuit is increased when each of the following elements is independently decreased except

Accepted Answer

The answer of The quality factor ("Q") of a simple...

Question 20

A large quality factor ("Q") for an RLC circuit means that

Accepted Answer

A large quality factor (Q) in an RLC circuit indicates that the circuit has a narrow bandwidth around its resonance frequency, which translates to a steep slope on its resonant curve. This means the circuit is highly selective, efficiently resonating at a specific frequency while attenuating frequencies away from resonance.

Quiz 32: Alternating Current Circuits

The impedance (Z) of an RLC circuit with 15 Ω\OmegaΩ resistor, 7 Ω\OmegaΩ capacitive reactance, and 12 Ω\OmegaΩ inductive reactance is