15.6 Transformers  (Page 4/9)

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?

A transformer is used to supply a 12-V model train with power from a 110-V wall plug. The train operates at 50 W of power. (a) What is the rms current in the secondary coil of the transformer? (b) What is the rms current in the primary coil? (c) What is the ratio of the number of primary to secondary turns? (d) What is the resistance of the train? (e) What is the resistance seen by the 110-V source?

The emf of an dc source is given by $v(t)=V_0\text{sin}\omega t,$ where $V_0=100\text{V}$ and $\omega =200\pi \text{rad/s}\text{.}$ Find an expression that represents the output current of the source if it is connected across (a) a $20\text{-}\mu \text{F}$ capacitor, (b) a 20-mH inductor, and (c) a $50\text{-}\text{Ω}$ resistor.

A 700-pF capacitor is connected across an ac source with a voltage amplitude of 160 V and a frequency of 20 kHz. (a) Determine the capacitive reactance of the capacitor and the amplitude of the output current of the source. (b) If the frequency is changed to 60 Hz while keeping the voltage amplitude at 160 V, what are the capacitive reactance and the current amplitude?

A 20-mH inductor is connected across an AC source with a variable frequency and a constant-voltage amplitude of 9.0 V. (a) Determine the reactance of the circuit and the maximum current through the inductor when the frequency is set at 20 kHz. (b) Do the same calculations for a frequency of 60 Hz.

A $30\text{-}\mu \text{F}$ capacitor is connected across a 60-Hz ac source whose voltage amplitude is 50 V. (a) What is the maximum charge on the capacitor? (b) What is the maximum current into the capacitor? (c) What is the phase relationship between the capacitor charge and the current in the circuit?

A 7.0-mH inductor is connected across a 60-Hz ac source whose voltage amplitude is 50 V. (a) What is the maximum current through the inductor? (b) What is the phase relationship between the current through and the potential difference across the inductor?

What is the impedance of an RLC series circuit at the resonant frequency?

What is the resistance R in the circuit shown below if the amplitude of the ac through the inductor is 4.24 A?

An ac source of voltage amplitude 100 V and frequency 1.0 kHz drives an RLC series circuit with $R=20\text{Ω}$ , $L=4.0\text{mH}$ , and $C=50\mu \text{F}$ . (a) Determine the rms current through the circuit. (b) What are the rms voltages across the three elements? (c) What is the phase angle between the emf and the current? (d) What is the power output of the source? (e) What is the power dissipated in the resistor?

In an RLC series circuit, $R=200\text{Ω}$ , $L=1.0\text{H}$ , $C=50\mu \text{F,}$ $V_0=120\text{V}$ , and $f=50\text{Hz}$ . What is the power output of the source?

A power plant generator produces 100 A at 15 kV (rms). A transformer is used to step up the transmission line voltage to 150 kV (rms). (a) What is rms current in the transmission line? (b) If the resistance per unit length of the line is $8.6\times {10}^{\mathrm{-8}}\text{Ω}\text{/m,}$ what is the power loss per meter in the line? (c) What would the power loss per meter be if the line voltage were 15 kV (rms)?