ok so a few questions here but ive tried all night to figure these out so please

Question

ok so a few questions here but ive tried all night to figure these out so please give explanations and thank u for ur time in advance!

A metal wire 9.50 m long has a circular cross section of radius 0.34 mm and an end-to-end resistance of 55.0 Ohms. The metal wire is then stretched uniformly so that its cross-section is still circular but its total length is now 23.75 m. What is the resistance of the wire after stretching? (Units: Ohm.)

A capacitor consisting of two concentric spheres of radius R1 and R2 = 3.50·R1 has a capacitance of C = 4.00 picoFarads and is charged to a potential difference of 60.0 Volts. Calculate the energy stored in the capacitor.
7.20×10-9 J

Calculate the charge on this capacitor, when the electrical energy stored is 11.0·10-8 Joules.
9.38×10-10 C

If the radius of the outer sphere is increased by a factor of 3.50 while keeping the charge on the plates constant, by what factor does the stored energy change?

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False.

True False  After being disconnected from the battery, increasing d decreases V.
True False  After being disconnected from the battery, inserting a dielectric with will increase V.
True False  With the capacitor connected to the battery, inserting a dielectric with will increase C.
True False  After being disconnected from the battery, decreasing d decreases C.
True False  With the capacitor connected to the battery, increasing d increases U.
True False  After being disconnected from the battery, inserting a dielectric with will increase U.

Two capacitors C1 = 4.1 F, C2 = 17.9 F are charged individually to V1 = 13.5 V, V2 = 8.0 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.
Calculate the final potential difference across the plates of the capacitors once they are connected.
9.025 V

Calculate the amount of charge (absolute value) that flows from one capacitor to the other when the capacitors are connected together.

By how much (absolute value) is the total stored energy reduced when the two capacitors are connected?

Explanation / Answer

here use the equation Qnet = CV

Q in serires remains same V in parallel remains same

so

Q1 = C1*V = 34.1 e-6 * 13.5 = = 4.6 e-4 C

Q2 = C2*V = 17.9 e-6* 8 = 1.432 e -4 C

Q = Q1 +Q2 = 4.6 +1.432 = 6.032 e -4 C , after connecting

use from V1 = Q1'/C1 and V2 = Q2'/C2 and V1 = V2 = V'

Q1' + Q2' = (C1+C2)*V' and V' = Q/C1+C2)

V' = 6.032 e -4 /( 4.1 e-6+17.9e-6) = 27.41 v

Now for renergy .

1) U1 = 0.5*Q1*v1 + 0.5*Q2*v2

U1 = (0.5*4.6 e -4*13.5)+(0.5*1.432 e -4 *8) = 3.68 m J

similarly for U2,

U2 = 0.5*(Q1'+Q2')*V'

U2 = 0.5*6.032 e -4 *27.41 = 8.266 m J

difference of eenrgy U = U2 - U1 = 8.266 - 3.68 = 4.58 mJ

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