S (1S points). An electrical cireuit with a mixed combination of capacitors conn

Question

S (1S points). An electrical cireuit with a mixed combination of capacitors connected to a pow supply of 10.0 V as shown in Figure. Find the equivalent capacitance and total charge sioreldl i the ciroui 24.0 pF 8.00 F 6 (15 points). Two identical point eharges (q +7.20 C are fixed at diagonally oposite corners of a square with sides of length 0.500 m. A test charge (q “ +2.40 pC) w ith a mass of 660 x10. kg is released from rest at one of empty corners of the square. Find the speed of the test charge when it reaches at infinity.

Explanation / Answer

5)

let C1 = 8 micro F

C2 = 24 micro F

C3 = 2 micro F

C4 = 4 micro F

her C1 and C2 are in series.

so, C12 = C1*C2/(C1 + C2)

= 8*24/(8+24)

= 6 micro F

The above combination is in parallel with C3 and C4.

so, Ceq = C12 + C3 + C4

= 6 + 2 + 4

= 12 micro F

Total charge stored, Q = Ceq*V

= 12*10

= 120 micro C or 1.2*10^-4 C

6) Potential at the corner, Vi = 2*k*Q/d

= 2*9*10^9*7.2*10^-6/0.5

= 2.592*10^5 V

Potential at infinite distance, Vf = 0

now use,

Workdone on test charge = gain in kinetic energy

qo*(Vi - Vf) = (1/2)*m*v^2

==> v = sqrt(2*qo*(Vi - Vf)/m)

= sqrt(2*2.4*10^-6*(2.592*10^5 - 0)/(6.6*10^-5))

= 137 m/s

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