Spherical Capacitor: Capacity, charge and voltage.

The radii of curvature of the spheres of a spherical capacitor is given and to find the charge, charge density and work done when it is connected to a battery.

The solution calculates the capacity of a spherical capacitor, charge on it when connected to a battery, charge densities on the spheres and the work done to bring a test charge across it.

Derive an expression for capacitance of spherical capacitor (inner and outer radii are R1 and R2 respectively) and show that in case of small distance between spheres (R1 ≈ R2) capacitance can be calculated using the expression for parallel plate capacitor.

I have a question that I need a little help with.
A 5.0 uf capacitor is connected to a 3.5 uf capacitor, and both of them are connected to a 6 volt battery.
1) what is the charge on each capacitor? What is the voltage on each capacitor?
2) With the battery still connected, the 3.5 uf cap is accidentally shorted out. As

Calculate the capacitance of a spherical shell capacitor given two plates one charged at +Q coulombs at a radius (a) from the center another plate charges at -Q coulombs at a radius (b) from the center and given that:
The voltage at a region between the spherical shells is given by
V(r) = kQ/r (a >

Please help with the following problem. Provide step by step calculations for each.
1. What is the energy in a 2 F capacitor at t = pi seconds if v(t) = cos(2t) ?
2. What is the energy in a 10 H inductor at t = pi seconds if i(t) = cos(2t) ?
3. The current flowing through a 1 H inductor is i(t) = 10*cos(20t) amps. Find th

See the attached file.
A large parallel plate capacitor is made up of two plane conducting sheets with seperation D, oneo f which has a small hemispherical boss of radius a on its inner surface (D >> a). The conductor with the boss is kept at zero potential, and the other conductor is at a potential such that far from the bos

Three capacitors(4.0, 6.0 and 15.0 Micro Farads) are connected in series across a 50 volts battery. Find the voltage across the 4.0 micro Farad capacitor. Answer in volts.

Please see the attached file for full problem description.
1. The voltage across a 5 uF capacitor is v(t) = 10sin(377t) V. What current flows through the capacitor?
2. The current flowing through a 5 F capacitor i(t) = 5e^(-2t) A. Write down the voltage and plot it for seconds. The capacitor is initially uncharged.
3.

A series circuits consists of two capacitors C1 = 3 uF, C2 =6 uF connected in series with a DC supply of V(supply) = 6V (SEE ATTACHMENT FOR CIRCUIT).
PART A: Determine the charge stored on C1 = 3 uF
PART B: Determine the charge stored on C2 = 6 uF
PART C: What is the voltage at point 1, the +ve side of C2?