(a)Two capacitors (C1=1.00 ?F and C2=2.00 ?F) are charged with Q1=3.00 ?C on the

Question

(a)Two capacitors (C1=1.00 ?F and C2=2.00 ?F) are charged with Q1=3.00 ?C on the positive plate of capacitor 1 and Q2=3.00 ?C on the positive plate of capacitor 2. Now if the positive plates are connected with each other and negative plates are connected with each other, what is (a) the final potential difference across each capacitor and (b) the total charge on the positive plate of capacitor 1?

(b)A copper cable hung on two power poles that are 121 m apart carries a current of 211 A. If the potential difference between the two ends of the cable is 0.400 V, what is the weight of the cable? The resistivity and density of copper are 1.72

Two capacitors (C1=1.00 ?F and C2=2.00 ?F) are charged with Q1=3.00 ?C on the positive plate of capacitor 1 and Q2=3.00 ?C on the positive plate of capacitor 2. Now if the positive plates are connected with each other and negative plates are connected with each other, what is (a) the final potential difference across each capacitor and (b) the total charge on the positive plate of capacitor 1? A copper cable hung on two power poles that are 121 m apart carries a current of 211 A. If the potential difference between the two ends of the cable is 0.400 V, what is the weight of the cable? The resistivity and density of copper are 1.72 times 10?8 ?m and 8.92 times 103 kg/m3, respectively. Three resistors and two batteries are connected in a circuit shown. If the resistances are R1=1.00 ?, R2=2.00 ?, R3=3.00 ?, and voltages of the batteries are V1=6.00 V and V2=12.00 V, find the currents going through the resistors, (a) I1, (b) I2, and (c) I3.

Explanation / Answer

a)

V1 = Q1/C1 = 3*10^-3/(1*10^-6) = 3*10^3 V

V2 = Q2/C2 = 3*10^-3/(2*10^-6) = 1.5*10^3 V

net charge will be same as 3 micro-C

b)

density = m/volume

v = m/d

also, v= A*L ... so,

==> A*L = m/d

==> A = m/(d*L)

now,

for resistace we have

R = V/I = resistivity*L/A

V*A/I = rho*L

V*m/(d*L) = rho*L*I

m = rho*L^2*d*I/V = 1.72*10^-8*8.92*10^3*121^2*211/0.4 = 1184.9 kg

c)

applying loops

let i1 and i2 is current in respective loops

for 1

i1*R1+(i1-i2)*R2 = V1-V2

i1*1+(i1-i2)*2 = 6-12

3*i1-2*i2 = -6 ...................(1)

for 2

(i2-i1)*2+i2*3 = V2 = 12

-2*i1+5*i2 = 12 ..................(2)

solving 1 and 2

i1 = -0.5454

i2 = 2.18182

so,

I1 = i1 = -5454 A

I2 = i2-i1 = 2.18182+0.5454 = 2.73 A

I3 = i2 = 2.18182 A

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