Problems

Calculate the reactance of a $5.0\text{-}\mu \text{F}$ capacitor at (a) 60 Hz, (b) 600 Hz, and (c) 6000 Hz.

Calculate the reactance of a 5.0-mH inductor at (a) 60 Hz, (b) 600 Hz, and (c) 6000 Hz.

At what frequency is the reactance of a $20\text{-}\mu \text{F}$ capacitor equal to that of a 10-mH inductor?

A $50\text{-}\text{Ω}$ resistor is connected across the emf $v\left(t\right)=\left(160\text{V}\right)\text{sin}\left(120\pi t\right)$. Write an expression for the current through the resistor.

A 100-mH inductor is connected across the emf of the preceding problem. (a) What is the reactance of the inductor? (b) Write an expression for the current through the inductor.

A resistor and capacitor are connected in series across an ac generator. The emf of the generator is given by $v(t)=V_0\text{cos}\omega t,$ where $V_0=120\text{V,}$ $\omega =120\pi \text{rad/s},$ $R=400\text{Ω}$, and $C=4.0\mu \text{F}$. (a) What is the impedance of the circuit? (b) What is the amplitude of the current through the resistor? (c) Write an expression for the current through the resistor. (d) Write expressions representing the voltages across the resistor and across the capacitor.

In an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively, an $R=500\text{Ω}\text{,}$ $L=0.20\text{H,}$ and $C=2.0\mu \text{F}\text{.}$ (a) What is the impedance of the circuit? (b) What is the amplitude of the current from the source? (c) If the emf of the source is given by $v\left(t\right)=\left(100\text{V}\right)\text{sin}1000\pi t$, how does the current vary with time? (d) Repeat the calculations with C changed to $0.20\mu \text{F}\text{.}$

For the circuit shown below, what are (a) the total impedance and (b) the phase angle between the current and the emf? (c) Write an expression for $i(t).$

Calculate the rms currents for an ac source is given by $v(t)=V_0\text{sin}\omega t,$ where $V_0=100\text{V}$ and $\omega =200\pi \text{rad/s}$ when connected across (a) a $20\text{-}\mu \text{F}$ capacitor, (b) a 20-mH inductor, and (c) a $50\text{-}\text{Ω}$ resistor.

For an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively; $R=500\text{Ω}$; and $L=0.20\text{H}$. Find the average power dissipated in the resistor for the following values for the capacitance: (a) $C=2.0\mu \text{F}$ and (b) $C=0.20\mu \text{F}\text{.}$

An RLC series circuit has an impedance of $60\text{Ω}$ and a power factor of 0.50, with the voltage lagging the current. (a) Should a capacitor or an inductor be placed in series with the elements to raise the power factor of the circuit? (b) What is the value of the reactance across the inductor that will raise the power factor to unity?

The resonant frequency of an RLC series circuit is $2.0\times {10}^3\text{Hz}\text{.}$ If the self-inductance in the circuit is 5.0 mH, what is the capacitance in the circuit?

For an RLC series circuit, $R=100\text{Ω}$, $L=150\text{mH}$, and $C=0.25\mu \text{F}\text{.}$ (a) If an ac source of variable frequency is connected to the circuit, at what frequency is maximum power dissipated in the resistor? (b) What is the quality factor of the circuit?

(a) What is the resonant frequency of a resistor, capacitor, and inductor connected in series if $R=100\text{Ω,}$ $L=2.0\text{H}$, and $C=5.0\mu \text{F}$? (b) If this combination is connected to a 100-V source operating at the resonant frequency, what is the power output of the source? (c) What is the Q of the circuit? (d) What is the bandwidth of the circuit?

An ac generator is connected to a device whose internal circuits are not known. We only know current and voltage outside the device, as shown below. Based on the information given, what can you infer about the electrical nature of the device and its power usage?

A step-up transformer connected to a 110-V line is used to supply a hydrogen-gas discharge tube with 5.0 kV (rms). The tube dissipates 75 W of power. (a) What is the ratio of the number of turns in the secondary winding to the number of turns in the primary winding? (b) What are the rms currents in the primary and secondary windings? (c) What is the effective resistance seen by the 110-V source?

A transformer is used to step down 110 V from a wall socket to 9.0 V for a radio. (a) If the primary winding has 500 turns, how many turns does the secondary winding have? (b) If the radio operates at a current of 500 mA, what is the current through the primary winding?