Exam 19: Dc Circuits

Three resistors of resistances $4.0 \Omega , 6.0 \Omega$ , and $10 \Omega$ are connected in parallel. If this combination is now connected in series with an ideal $12 - \mathrm { V }$ battery and a $2.0 - \Omega$ resistor, what is the current through the $10 - \Omega$ resistor?

A circuit contains two batteries and a $2.0 - \Omega$ resistor as shown in the figure. The emfs and internal resistances of these batteries are indicated in the figure, and all numbers are accurate to two significant figures. What are the terminal voltages of (a) the $6.0$ - $\mathrm { V }$ battery and (b) the 12-V battery?

An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V. What must be the ratio of the number of turns in the secondary to the number of turns in the primary?

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time $t = 0 \mathrm {~s}$ , the switch is closed. Which of the graphs below best describes the potential difference $V$ across the capacitor as a function of time $t$ ?

A series circuit consists of a $2.5 - \mu \mathrm { F }$ capacitor, a 7.6- $\mathrm { M } \Omega$ resistor, and an ideal $6.0 - \mathrm { V }$ dc power source. (a) What is the time constant for charging the capacitor? (b) What is the potential difference across the capacitor $25 \mathrm {~s}$ after charging begins?

The current through a $50 - \Omega$ resistor is $I = ( 0.80 \mathrm {~A} ) \sin ( 240 t )$ , where $t$ is measured in seconds. What is the rms current?

If emf of the ideal battery is $V = 100 \mathrm {~V}$ , what is the potential difference across $R _ { 5 }$ for the circuit shown in the figure?

A galvanometer that gives a full-scale deflection when $150 \mu \mathrm { A }$ runs through it is used to make an ammeter that reads a maximum of $1.00 \mathrm {~A}$ . To do this, a $3.3 - \mathrm { m } \Omega$ shunt was required. What is the resistance of just the galvanometer?

A simple series circuit contains a $6.0 - \Omega$ resistor, an ideal $15 - \mathrm { V } D C$ power supply, and an $18 - \mathrm { H }$ inductor. What the time constant of this circuit?

Three resistors with resistances of $2.0 \Omega , 6.0 \Omega$ , and $12 \Omega$ are connected across an ideal dc voltage source $V$ as shown in the figure. If the total current through the circuit is $I = 2.0 \mathrm {~A}$ , what is the applied voltage $V$ ?

An ac generator consists of 100 loops of wire, each of area $0.090 \mathrm {~m} ^ { 2 }$ , and has a total resistance $12 \Omega$ The loops rotate about a diameter in a magnetic field of $0.50 \mathrm {~T}$ at a constant angular speed of 60 revolutions per second. Find the maximum induced emf in the generator.

You buy a AA battery in the store, and it is marked $1.5 \mathrm {~V}$ . If this marking is strictly accurate, while this battery is fresh

As shown in the figure, an ac source whose rms voltage is $80 \mathrm {~V}$ is in series with a $100 - \Omega$ resistor and a capacitor whose reactance is $200 \Omega$ at the frequency of the source. What is the rms voltage across the capacitor?

A $2.0 - \mu \mathrm { F }$ capacitor and a 4.0- $\mu \mathrm { F }$ capacitor are connected in series across an $8.0$ - $\mathrm { V }$ potential source. What is the charge on the $2.0 - \mu \mathrm { F }$ capacitor?

A conducting rod whose length is $\ell = 25 \mathrm {~cm}$ is placed on a $U$ -shaped metal wire that is connected to a lightbulb having a resistance of $8.0 \Omega$ as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength $0.40 \mathrm {~T}$ is applied perpendicular to and out of the paper. An external applied force moves the rod to the left with a constant speed of $12 \mathrm {~m} / \mathrm { s }$ . What are the magnitude and direction of the induced current in the circuit?

A 4.0-µF capacitor and an 8.0-µF capacitor are connected together. What is the equivalent capacitance of the combination if they are connected (a) in series or (b) in parallel?

What is the inductive reactance of a $2.50 - \mathrm { mH }$ coil at $1000 \mathrm {~Hz}$ ?

What is the impedance of an ac series circuit with $12.0 \Omega$ of resistance, $15.0 \Omega$ of inductive reactance, and $10.0 \Omega$ of capacitive reactance?

Inductors store energy by accumulating excess charge within their coils.

An ac generator with a total resistance of $12 \Omega$ contains 100 flat loops of wire, each with an area of $0.090 \mathrm {~m} ^ { 2 }$ . The loops rotate at $60 \mathrm { rev } / \mathrm { s }$ in a magnetic field of magnitude $0.50 \mathrm {~T}$ . What is the maximum possible induced current?