Exam 19: Dc Circuits

A group of $1.0 - \mu \mathrm { F } , 2.0 - \mu \mathrm { F }$ , and $3.0 - \mu \mathrm { F }$ capacitors is connected in parallel across a $24 - \mathrm { V }$ potential difference (a battery). How much energy is stored in this three-capacitor combination when the capacitors are fully charged?

An ideal solenoid has a self-inductance $L$ . If you now double its radius and its length, but do not change the number of coils, what will its self-inductance be?

In the circuit shown in the figure, the $60 - \mathrm { Hz }$ ac source has a voltage amplitude of $120 \mathrm {~V}$ , the capacitive reactance is $750 \Omega$ , the inductive reactance is $290 \Omega$ , and the resistance is $500 \Omega$ . What is the inductance $L$ of the inductor?

A series $R L C$ circuit has a $100 - \Omega$ resistor, a $0.100 - \mu \mathrm { F }$ capacitor and a $2.00 - \mathrm { mH }$ inductor connected across a 120-V rms ac voltage source operating at $1000 / \pi \mathrm { Hz }$ . What is the resonant frequency of this circuit?

Identical ideal batteries are connected in different arrangements to the same light bulb, as shown in the figure. For which arrangement will the bulb shine the brightest?

A $60.0 - \mu \mathrm { F }$ capacitor is in series with a $100 - \Omega$ resistor connected across an ac source of frequency $120 \mathrm {~Hz}$ . What is the phase angle?

The mutual inductance between two coils is 10 mH. The current in the first coil changes uniformly from 2.7 A to 5.0 A in 160 ms. If the second coil has a resistance of 0.60 Ω, what is the magnitude of the induced current in the second coil?

A $120 - \mathrm { V }$ rms signal at $60.0 \mathrm {~Hz}$ is applied across a series combination of a $30.0 - \mathrm { mH }$ inductor and a resistor. If the rms value of the current in this circuit is $0.600 \mathrm {~A}$ , what is the resistance of the resistor?

A galvanometer with a coil resistance of $40.0 \Omega$ deflects full scale for a current of $2.0 \mathrm {~mA}$ . What series resistance should be used with this galvanometer in order to construct a voltmeter that deflects full scale for $50 \mathrm {~V}$ ?

In the circuit shown in the figure, the resistor $R$ has a variable resistance. As $R$ is decreased, what happens to the currents?

The power factor of an ac $R L$ circuit with a $100 - \Omega$ resistor and a certain inductor is $0.60$ . What is the impedance of the circuit?

Inductors cannot store energy because they cannot store charge.

As shown in the figure, a metal bar is in contact with a pair of parallel rails. A steady, uniform, magnetic field $B$ is present directed to the right. The bar is moving upward with velocity of magnitude $v$ . What is the polarity of the induced emf in terminals $X$ and $Y$ ?

A circular conducting loop with a radius of $0.50 \mathrm {~m}$ and a small gap filled with a $10.0 - \Omega$ resistor is oriented in the $x y$ -plane. If a uniform magnetic field of $1.0 \mathrm {~T}$ , making an angle of $30 ^ { \circ }$ with the $z$ -axis, increases to $10.0 \mathrm {~T}$ , in $4.0 \mathrm {~s}$ , what is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance?

A flat rectangular coil with dimensions of $8.0 \mathrm {~cm} \times 10 \mathrm {~cm}$ is dropped from a zero magnetic field position into a 1.4-T magnetic field in $0.10 \mathrm {~s}$ . The coil has 60 turns and is perpendicular to the magnetic field. What is the average induced emf in the coil as a result of this action?

The impedance of an $R C$ circuit containing a $40.0 - \mu \mathrm { F }$ capacitor is $800 \Omega$ . If the frequency of the applied ac voltage is $18.0 \mathrm {~Hz}$ , what is the resistance of the resistor?

A galvanometer has a coil with a resistance of $24.0 \Omega$ , and a current of $180 \mu \mathrm { A }$ causes full-scale deflection. If the galvanometer is to be used to construct an ammeter that deflects full scale for $10.0 \mathrm {~A}$ , what shunt resistor is required?

A 9-V battery is hooked up to two resistors in series using wires of negligible resistance. One has a resistance of $5 \Omega$ , and the other has a resistance of $10 \Omega$ . Several locations along the circuit are marked with letters, as shown in the figure. Which statements about this circuit are true? (There could be more than one correct choice.)

Two resistors with resistances of $5.0 \Omega$ and $9.0 \Omega$ are connected in parallel. A 4.0- $\Omega$ resistor is then connected in series with this parallel combination. An ideal 6.0-V battery is then connected across the series-parallel combination. What is the current through (a) the $4.0 - \Omega$ resistor and (b) the $5.0 - \Omega$ resistor?

A round flat conducting loop is placed perpendicular to a uniform $0.50 \mathrm {~T}$ magnetic field. If the area of the loop increases at a rate of $3.0 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 } / \mathrm { s }$ , what is the induced emf in the loop?