Exam 29: Potential and Field

An air-filled capacitor stores a potential energy of 6.00 mJ due to its charge. It is accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air it is 1.0006.)

Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points a and b?

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original capacitance was C₀, what is the new capacitance?

Two capacitors of capacitance 6.00 μF and 8.00 μF are connected in parallel. The combination is then connected in series with a 12.0-V voltage source and a 14.0-μF capacitor, as shown in the figure. (a) What is the equivalent capacitance of this combination? (b) What is the charge on the 6.00-μF capacitor? (c) What is the potential difference across the 6.00-μF capacitor?

Three capacitors, with capacitances C₁ = 4.0 μF, C₂ = 3.0 μF, and C₃ = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor C₂?

Equal but opposite charges Q are placed on the square plates of an air-filled parallel-plate capacitor. The plates are then pulled apart to twice their original separation, which is small compared to the dimensions of the plates. Which of the following statements about this capacitor are true? (There may be more than one correct choice.)

The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is the total energy stored in the seven capacitors?

A 6.0-μF air-filled capacitor is connected across a 100-V voltage source. After the source fully charges the capacitor, the capacitor is immersed in transformer oil (of dielectric constant 4.5). How much ADDITIONAL charge flows from the voltage source, which remained connected during the process?

The graph in the figure shows the variation of the electric potential V(x) (in arbitrary units) as a function of the position x (also in arbitrary units). Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis?

In the circuit shown in the figure, all the capacitors are air-filled. With the switch S open, the 40.0-µF capacitor has an initial charge of 5.00 µC while the other three capacitors are uncharged. The switch is then closed and left closed for a long time. Calculate the initial and final values of the total electrical energy stored in these four capacitors.

If the potential in a region is given by V(x,y,z) = xy - 3z^-2, then the y component of the electric field in that region is

A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

Five capacitors are connected across a potential difference V_ab as shown in the figure. Because of the dielectrics used, each capacitor will break down if the potential across it exceeds 30.0 V. The largest that V_ab can be without damaging any of the capacitors is closest to

A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

The potential as a function of position x is shown in the graph in the figure. Which statement about the electric field is true?

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m², and the separation of the plates is 0.080 mm. An electric field of 5.3 × 10⁶ V/m is present between the plates. What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Four capacitors are connected across a 90-V voltage source as shown in the figure. (a) What is the charge on the 4.0-μF capacitor? (b) What is the charge on a 2.0-μF capacitor? (c) What is the charge on the 3.0-μF capacitor? (d) What is the potential difference across the 6.0-μF capacitor?