A 2.2 mu F capacitor is initially uncharged, and then charged by a 24 V power su

Question

A 2.2 mu F capacitor is initially uncharged, and then charged by a 24 V power supply running through a resistor. After 16.4 seconds, the voltage across the capacitor has increased to 21.6 V. What is the resistance of the resistor? Consider this page as the x - y plane. Two wires are coming out of the page, at (1, 0) cm and (-1, 0) cm. Using the principle of superposition, calculate the direction of the magnetic field at the origin if: (a) The wires are carrying equal currents out of the page (or in the positive z direction). (b) The wires are carrying equal currents, with the current at (1, 0) cost of the page (+z), and the current at (-1, 0) into the page (-z).

Explanation / Answer

1)

In a capacitor circuit

the potential across the capcitor increases as vc = E*(1-e^-(t/RC))

Vc = 21.6 V

21.6 = 24*(1-e^-(16.4/(R*2.2*10^-6)))

R = 3.24*10^6 ohms

(2)

(a)

wire 1 at ( 1 , 0)

wire 2 ar ( -1 , 0)

B1y = -uo*I/(2*pi*0.01)

B2y = + Uo*I/(2*pi*0.01)

Bnet = B1 + B2 = 0

no direction

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(b)

B1y = -uo*I/(2*pi*0.01)

B2y = - Uo*I/(2*pi*0.01)

Bnet = B1 + B2 = -2*uo*I/(2*pi*0.01)

Bnet along -y direction

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