9. Consider the two long, cylindrical conductor, separated by a distance d form a capacitor, Cylinder 1 has charge density A and radius bị and Cylinder 2 has charge density -d and radius b2. Show that the capacitance per unit length is given approximately by C = T€0 ( In where b is the geometric mean
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- Consider the following. (LetC1 30.60 µF and C, = 24.60 μF.) 6.00 µF C, + 9.00 V (a) Find the equivalent capacitance of the capacitors in the figure. µF (b) Find the charge on each capacitor. on the right 30.60 µF capacitor on the left 30.60 µF capacitor on the 24.60 µF capacitor on the 6.00 µF capacitor (c) Find the potential difference across each capacitor. on the right 30.60 µF capacitor V on the left 30.60 µF capacitor V on the 24.60 µF capacitor V on the 6.00 µF capacitor VA 1 megabit computer memory chip contains many 57.0 fF capacitors. Each capacitor has a plate area of 22.0 x 1012 m2. Determine the plate separation of such a capacitor (assume a parallel-plate configuration). The order of magnitude of the diameter of an atom is 1010 m = 0.100 nm. Express the plate separation in nanometers. nmThere are two capacitors. If they are connected in parallel, the equivalent electricity capacity is 9.00 pF, and if they are connected in series, the equivalent electricity capacity is 2.00 pF. Find the capacitance of each capacitor.
- A parallel plate capacitor is made up of two metal squares with sides of length 7.3 cm, separated by a distance 4.6 mm. When a voltage 139 V is set up across the terminals of the capacitor, the charge stored on the positive plate is equal to nC. Give your answer to 2 decimal places.A system of capacitors is shown below. What is the equivalent capacitance of the system is the individual capacitors are; Express the answer in microFarads. For example, if the answer came out to be 4.98 X 10-7 F, this is the same as 49.8 microFarads. You would then answer with the numeric value of 4.98. C₁ = 9 x 10-6 F C₂ = 8.8 x 10-6 F C3 = 3.6 x 10-6 F C4 = 4 x 10-6 F C5 = 8.2 x 10-6 F C1 C3 C4 C5 12 volts C2A spherical capacitor consists of a spherical conducting shell of radius bb and charge −Q concentric with a smaller conducting sphere of radius a and charge +Q. Enter an expression for the capacitance of this device in terms of Coulomb's Constant ke (just type "k" with no subscript) and the two radii a and b. HINT: you may need to apply a negative sign to your final expression to be sure the capacitance comes out positive! Look at your answer and think about which radii is larger.
- Storm clouds build up large negative charges. The charges dwell in charge centers, regions of concentrated charge. Suppose a cloud has -25 C in a 1.0@km@diameter spherical charge center located 10 km above the ground, as sketched is shown. The negative charge center attracts a similar amount of positive charge that is spread on the ground below the cloud.The charge center and the ground function as a charged capacitor, with apotential difference of approximately 4 x 108 V. The large electric field between these two “electrodes” may ionize the air, leading to a conducting path between the cloud and the ground. Charges will flow along this conducting path, causing a discharge of the capacitor—a lightning strike. What is the approximate capacitance of the charge center + ground system?A. 6 x 10-8 F B. 2 x 107 F C. 4 x 106 F D. 8 x 106 F2. In lecture we saw parallel plate and coaxial cylindrical capacitors. We can also have spherical capacitors! Consider a conducting sphere with radius a and total charge Q enclosed within a concentric hollow spherical conducting shell with radius 6 and a total charge -Q. For parts a) and b), the region between the conductors (a < r < b) is empty (vacuum). a) Find an expression for the capacitance of a spherical capacitor. Is it geometric as we expect? b) Find an expression for the energy stored by the spherical capacitor first by using U (just replace C by your answer from part a)) and second by integrating the energy density u of the electric field over all space. Do your answers agree? = 20 c) Now suppose the region between the conductors is filled with a dielectric with dielectric constant ‹ = 3. What is the bound charge per unit area near the inner sphere (at r = = a) and near the outer shell (at r = b)? What is the total bound charge at each surface (expressed as a fraction of…A parallel-plate capacitor has square plates that have edge length equal to 1.20×10^2cm and are separated by 1.00 mm. It is connected to a battery and is charged to 12.0 V. 1)How much energy is stored in the capacitor? (Express your answer to three significant figures.)
- A system of capacitors is shown below. What is the equivalent capacitance of the system is the individual capacitors are; Express the answer in microFarads. For example, if the answer came out to be 4.98 X 10-7 F, this is the same as 49.8 microFarads. You would then answer with the numeric value of 4.98. C1 = 5.5 x 10-6 F C2 = 5.7 x 10-6 F C3 = 8 x 10-6 F C4 = 4.5 x 10-6 F C5 = 2.1 x 10-6 FA solid cylindrical conductor of radius 2.1 cm is coaxial with a cylindrical shell of negligible thickness, radius 2.3 cm. Find the capacitance ( in units of nF) of this cylindrical capacitor if its length is 51.8 m. Select one: A. 41.99 B. 21.27 C. 14.56 D. 31.63 E. 47.17The ratio of the radii of the spheres is 2.935. What is the radius (in m) of the smaller sphere if the connected spheres have an equivalent capacitance of 41.11nF?