Two conducting rails 30 cm apart rest on a 5.0$\degree$ ramp. They are joined at the bottom by a $0.60 ~\Omega$ resistor, and at the top a copper bar of mass $0.040$ kg is laid across the rails. The whole apparatus is immersed in a vertical $0.55 ~\mathrm{T}$ field. What is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

Lightning sometimes happens between clouds. Suggest a possible way that a discharge can occur between clouds.

A resistor dissipates 723 joules of energy in 3 minutes and 47 seconds. Calculate the rate at which energy is being transferred to this resistor in joules per second. What is its power dissipation in watts?

Two resistors are connected in series to a battery with an emf of $12 \mathrm{~V}$. The voltage across the first resistor is $2.7 \mathrm{~V}$ and the current through the second resistor is $0.15 \mathrm{~A}$. Find the resistance of the two resistors.

A current of $4.82 \mathrm{~A}$ exists in a $12.4 \mathrm{\Omega}$ resistor for $4.60 \mathrm{~min}$. (a) How much charge and (b) how many electrons pass through any cross section of the resistor in this time?

Pete is designing a voltage divider using a 12-V battery and a $82-\Omega$ resistor as $R_{\mathrm{B}}$. What resistor should be use as $R_{\mathrm{A}}$ if the output voltage across $R_{\mathrm{B}}$ is to be 4.0 V?

a) In the given circuit, the thermistor has a resistance of $200 \Omega$.

i) Calculate the current through the resistor and thermistor.

ii) Calculate the potential difference across the $1000 \Omega$ resistor.

b) The temperature of the thermistor decreases so that the potential difference across the $1000 \Omega$ resistor becomes $4 \mathrm{~V}$. Calculate the new value of the resistance of the thermistor.

A long, narrow resistor is placed in a series circuit along with a short, wide resistor made of the same material. Which will have a greater electric potential drop across it? Explain your reasoning.

A 12.0-V battery is attached to a 2.00-mF capacitor and a 100.- $\Omega$ resistor. Once the capacitor is fully charged, what is the energy stored in it? What is the energy dissipated as heat by the resistor as the capacitor is charging?

Set up systems of equations and solve by Gaussian elimination. The voltage across an electric resistor equals the current (in A) times the resistance (in $\ohm$). If a current of 3.00 A passes through each of the two resistors, the sum of the voltages is 10.5 V. If 2.00 A passes through the first resistor and 4.00 A passes through the second resistor, the sum of the voltages is 13.0 V. Find the resistances.

The output voltage of an AC generator is given by $\Delta v = ( 170 \mathrm { V } ) \sin ( 60 \pi t )$. The generator is connected across a 20.0-$\Omega$ resistor. Find the rms voltage across the resistor.

What happens to the resistance of a common ohmic resistor, if it is heated?

Air is pumped into the top of the tank so that the pressure at $B$ is $40\ \mathrm{kPa}$. Calculate the discharge of the water as a function of the height $h$. Plot the discharge (vertical axis) versus $h$ for $1 \mathrm{~m} \leq h \leq 6 \mathrm{~m}$. Give values for increments of $\Delta h=1 \mathrm{~m}$.

The voltage across a $10-\Omega$ resistor is given by $v(t) = 5 \sin (2 \pi \mathrm{t}) \mathrm{V}.$ Determine the energy delivered to the resistor between t = 0 and t = 10 s.