Exam 19: Dc Circuits

It is known that birds can detect the earth's magnetic field, but the mechanism of how they do this is not known. It has been suggested that perhaps they detect a motional emf as they fly north to south, but it turns out that the induced voltages are small compared to the voltages normally encountered in cells, so this is probably not the mechanism involved. To check this out, calculate the induced voltage across the wingtips of a wild goose with a wingspan of $1.2$ mif it is flying directly south at $13 \mathrm {~m} / \mathrm { s }$ at a point where the earth's magnetic field is $5.0 \times 10 ^ { - 5 } \mathrm {~T}$ directed downward from the horizontal by $40 ^ { \circ }$ .

A heating element having a resistance (at its operating temperature) of $148 \Omega$ is connected to a battery having an emf of $523 \mathrm {~V}$ and unknown internal resistance.It is found that heat energy is being generated in the resistance of the heating element at a rate of $66.0 \mathrm {~W}$ . What is the rate at which heat energy is being generated in the internal resistance of the battery?

A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of $0.40 \mathrm {~T}$ , as shown in the figure. The length of the loop $L$ is $0.16 \mathrm {~m}$ and its width $w$ is $0.040 \mathrm {~m}$ . What is the magnetic flux through the loop when the plane of the loop is parallel to the magnetic field?

For the circuit shown in the figure, $R _ { 1 } = 50 \Omega , R _ { 2 } = 20 \Omega , R _ { 3 } = 35 \Omega , R _ { 4 } = 10 \Omega , R _ { 5 } = 68 \Omega$ , $I _ { 1 } = 0.111 \mathrm {~A} , I _ { 2 } = 0.142 \mathrm {~A}$ , and the batteries are ideal. (a) Determine $V _ { 1 }$ and $V _ { 2 }$ . (b) What is the potential difference across $R _ { 4 }$ ?

The figure shows a series ac circuit. The inductor has a reactance of $60 \Omega$ and an inductance of 210 $\mathrm { mH }$ . A $30 - \Omega$ resistor and a capacitor whose reactance is $80 \Omega$ are also in the circuit, and the rms current in the circuit is $2.2 \mathrm {~A}$ . What is the phase angle of the circuit?

A 5- $\mu \mathrm { F }$ , a $7 - \mu \mathrm { F }$ , and an unknown capacitor $C \mathrm { X }$ are connected in parallel between points $a$ and $b$ as shown in the figure. What do you know about the equivalent capacitance $C _ { a b }$ between $a$ and $b$ ? (There could be more than one correct choice.)

A series circuit consists of a $100 - \Omega$ resistor, a $10.0 - \mu \mathrm { F }$ capacitor, and a $0.350 - \mathrm { H }$ inductor. The circuit is connected to a $120 - \mathrm { V } r m s , 60 - \mathrm { Hz }$ power supply. What is the rms current in the circuit?

A multiloop circuit is shown in the figure, but some quantities are not labeled. Find the emf $\varepsilon$ if the batteries are ideal. (It is not necessary to solve the entire circuit.)

In the circuit shown in the figure, $R _ { 1 } = R _ { 2 } = 90.0 \Omega , R _ { 3 } = R _ { 4 } = 20.0 \Omega , V _ { 1 } = 7.0 \mathrm {~V} , V _ { 2 } = 8.0 \mathrm {~V}$ , and the batteries are both ideal. What current does the ammeter read?

A $5.0 - \mu \mathrm { F }$ capacitor and a 7.0- $\mu \mathrm { F }$ capacitor are connected in series across an $8.0$ - $\mathrm { V }$ potential source. What is the potential difference across the $5.0 - \mu \mathrm { F }$ capacitor?

A pure capacitor is connected to an ac power supply. In this circuit, the current

The potential applied to a $20 - \Omega$ resistor is $v = ( 60 \mathrm {~V} ) \cos ( 33 t )$ . What is the rms current through this resistor?

A potential difference of $V = 100 \mathrm {~V}$ is applied across two capacitors in series, as shown in the figure. If $C _ { 1 } = 10.0 \mu \mathrm { F }$ and the voltage drop across it is $75 \mathrm {~V}$ , what is the capacitance of $C _ { 2 }$ ?

A number of resistors are connected across points $A$ and $B$ as shown in the figure. What is the equivalent resistance between points $\mathrm { A }$ and $\mathrm { B }$ ?

For the circuit shown in the figure, the current in the $8.0 - \Omega$ resistor is $0.50 \mathrm {~A}$ . What is the current in the $2.0 - \Omega$ resistor? All the numbers shown are accurate to two significant figures.

For the circuit shown in the figure, $C = 13 \mu \mathrm { F }$ and $R = 7.6 \mathrm { M } \Omega$ . Initially the switch $\mathrm { S }$ is open with the capacitor charged to a voltage of $80 \mathrm {~V}$ . The switch is then closed at time $t = 0.00 \mathrm {~s}$ . What is the charge on the capacitor $40 \mathrm {~s}$ after closing the switch?

Draw a circuit with a battery connected to four resistors, $R _ { 1 } , R _ { 2 } , R _ { 3 }$ , and $R _ { 4 }$ , as follows. Resistors $R _ { 1 }$ and $R _ { 2 }$ are connected in parallel with each other, resistors $R _ { 3 }$ and $R _ { 4 }$ are connected in parallel with each other, and both parallel sets of resistors are connected in series with each other across the battery.

Draw a circuit consisting of a battery connected to two resistors, $R _ { 1 }$ and $R _ { 2 }$ , in series with each other and a capacitor $C$ connected across the resistors.

What is the impedance at $1500 \mathrm {~Hz}$ if a $100 - \Omega$ resistor, $20 - \mathrm { mH }$ coil, and $1.0 - \mu \mathrm { F }$ capacitor are connected in series?

Determine the current in the $8.0 - \Omega$ resistor for the circuit shown in the figure. Assume that the batteries are ideal and that all numbers are accurate to two significant figures.