Question 1

The current through a 50-Ω resistor is I = (0.80 A) sin(240t),where t is measured in seconds. How much power on average is dissipated in the resistor?

Accepted Answer

The average power dissipated in a resistor, when the current is sinusoidal, is given by $P_{avg} = \frac{1}{2}I_{rms}^2R$, where $I_{rms}$ is the root mean square of the current and $R$ is the resistance. For a sinusoidal current $I = I_0 \sin(\omega t)$, $I_{rms} = \frac{I_0}{\sqrt{2}}$. Here, $I_0 = 0.80 A$, so $I_{rms} = \frac{0.80 A}{\sqrt{2}}$. Plugging into the formula for average power, $P_{avg} = \frac{1}{2}(\frac{0.80}{\sqrt{2}})^2 \times 50 = 16 W$.

Question 2

What is the rms current through a 0.0010-μF capacitor at 1000 Hz and 5.0 V?

Accepted Answer

The rms current through a capacitor is given by the formula I = VωC, where I is the rms current, V is the rms voltage, ω is the angular frequency (ω = 2πf, with f being the frequency), and C is the capacitance. For a 0.0010-μF (or 1.0 x 10^-9 F) capacitor at 1000 Hz and 5.0 V, ω = 2π(1000) = 2000π rad/s. Therefore, I = 5.0 x 2000π x 1.0 x 10^-9 = 31.4 x 10^-6 A, or approximately 31 μA.

Question 3

The reactance of a capacitor is 
At a frequency of 
What is the capacitance?

Accepted Answer

The answer of The reactance of a capacitor is 
At...

Question 4

A 6.0-μF capacitor is connected to an ac signal with a frequency of 60 Hz.If the maximum voltage applied to the capacitor is 8.0 V,what is its capacitive reactance?

Accepted Answer

The answer of A 6.0-μF capacitor is connected to an...

Question 5

In the circuit shown in the figure,the 60-Hz ac source has a voltage amplitude of 120 V,the capacitive reactance is 
The inductive reactance is 
And the resistance is 
What is the capacitance C of the capacitor?

Accepted Answer

The answer of In the circuit shown in the figure,the...

Question 6

A 120-V rms voltage is applied across a 6.0-μF capacitor.If the frequency of the generator is 60 Hz,what is the rms value of the current in the circuit?

Accepted Answer

The rms current in a capacitive circuit is given by $I_{rms} = V_{rms} \times \omega C$, where $V_{rms}$ is the rms voltage, $\omega$ is the angular frequency ($\omega = 2\pi f$, with $f$ being the frequency), and $C$ is the capacitance. Given $V_{rms} = 120\,V$, $C = 6.0\,\mu F = 6.0 \times 10^{-6}\,F$, and $f = 60\,Hz$, we find $\omega = 2\pi \times 60$. Thus, $I_{rms} = 120 \times 2\pi \times 60 \times 6.0 \times 10^{-6} = 0.27\,A$.

Question 7

At what frequency will the capacitive reactance of a 0.010-μF capacitor be 100 Ω?

Accepted Answer

Capacitive reactance is given by 1/(2πfC), where f is the frequency and C is the capacitance. So, 100 Ω = 1/(2πf * 0.010 μF). Solving for f, we get f = 16 kHz.

Question 8

A 10-Ω resistor is connected to a 120-V ac power supply.What is the peak current through the resistor?

Accepted Answer

We can use Ohm's law for an AC circuit to find the peak current:

Vpeak = Ipeak * R

Rearranging the equation to solve for Ipeak:

Ipeak = Vpeak / R

The peak voltage for a 120V AC power supply is:

Vpeak = 120V * sqrt(2) = 169.7V

Substituting into the equation above:

Ipeak = 169.7V / 10Ω = 16.97A

Rounding to the nearest whole number, we get:

Ipeak = 17A

Therefore, the answer is B).

Question 9

What is the peak voltage in an ac circuit where the rms voltage is 120 V?

Accepted Answer

The peak voltage (V_peak) in an AC circuit is calculated from the RMS voltage (V_rms) using the formula V_peak = V_rms * sqrt(2). For an RMS voltage of 120 V, the peak voltage is 120 V * sqrt(2) ≈ 170 V.

Question 10

What is the inductive reactance of a 2.50-mH coil at 1000 Hz?

Accepted Answer

Inductive reactance (X_L) is calculated using the formula X_L = 2πfL, where f is the frequency in hertz and L is the inductance in henries. Substituting the given values, X_L = 2 * π * 1000 * 2.50e-3 = 15.7 Ω.

Question 11

What is the reactance of a 1.0-mH inductor at 60 Hz?

Accepted Answer

The reactance of an inductor is calculated using the formula $X_L = 2\pi fL$, where $f$ is the frequency in hertz and $L$ is the inductance in henries. Plugging in the given values, $X_L = 2\pi(60)(0.001) = 0.377$, which rounds to 0.38 Ω.

Question 12

An alternating current is supplied to an electronic component with a rating that the voltage across it can never,even for an instant,exceed 16 V.What is the highest rms voltage that can be supplied to this component while staying below the voltage limit?

Accepted Answer

The answer of An alternating current is supplied to an...

Question 13

At what frequency is the reactance of a 20.0-mH inductor equal to 120 Ω?

Accepted Answer

The answer of At what frequency is the reactance of...

Question 14

The current through a 50-Ω resistor is I = (0.80 A) sin(240t),where t is measured in seconds.What is the rms current?

Accepted Answer

The formula for calculating the rms current for an AC circuit is Irms = Ipeak/√2. In this case, the peak current is 0.8 A. Thus, 
Irms = (0.8 A)/√2 ≈ 0.57 A. Therefore, the best choice is A.

Question 15

The capacitive reactance of a 44-μF capacitor in an ac circuit is 6.0 × 
Ω.What is the frequency of the applied signal?

Accepted Answer

The answer of The capacitive reactance of a 44-μF capacitor...

Question 16

A 150-W lamp is placed into a 120-V ac outlet.What is the peak current?

Accepted Answer

The answer of A 150-W lamp is placed into a...

Question 17

What is the reactance of a 20-mH inductor at a frequency of 60 Hz?

Accepted Answer

The reactance of an inductor is calculated using the formula $X_L = 2\pi fL$, where $f$ is the frequency in hertz and $L$ is the inductance in henries. Plugging in the given values, $X_L = 2\pi \times 60 \times 0.02 = 7.54 \Omega$, which rounds to 7.5 Ω.

Question 18

At what frequency does a 10-μF capacitor have a reactance of 1200 Ω?

Accepted Answer

The capacitive reactance (Xc) is given by the formula Xc = 1/(2πfC). Solving for frequency (f), f = 1/(2π * 1200 Ω * 10 * 10^-6 F) ≈ 13 Hz.

Question 19

A 120-V rms voltage at 60.0 Hz is applied across an inductor,capacitor and a 100-Ω resistor in series.If the maximum value of the current in this circuit is 1.60 A,what is the rms value of the current in this circuit?

Accepted Answer

The rms value of the current is equal to the maximum value of the current divided by the square root of 2. Therefore, the rms value of the current is 1.60 A / sqrt(2) = 1.13 A.

Question 20

In the circuit shown in the figure,the 60-Hz ac source has a voltage amplitude of 120 V,the capacitive reactance is 
The inductive reactance is 
And the resistance is 
What is the inductance L of the inductor?

Accepted Answer

The answer of In the circuit shown in the figure,the...

Quiz 24: Alternating-Current Circuits

The current through a 50-Ω resistor is I = (0.80 A) sin(240t) ,where t is measured in seconds. How much power on average is dissipated in the resistor?