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Here\'s a circuit built from five 10 omega resistors. How much power is used by

ID: 1441120 • Letter: H

Question

Here's a circuit built from five 10 omega resistors. How much power is used by the resistor in the middle? A 10 V battery is used to charge a 5 mu F capacitor through a 3k omega resistor. At 0.01 seconds after the capacitor starts charging: What is the voltage on the capacitor? How much current is flowing in the circuit? Three wires, each carrying 10 A of current, cross in the shape of an equilateral triangle. What is the magnetic field in the center of the triangle? You should give both the magnitude and the direction.

Explanation / Answer

1)

let the current in the

Req = (10 || 10 ) + 10 + (10 || 10 )

Req = 10 * 10/(10 + 10) + 10 + 10 * 10/(10 + 10)

Req = 20 ohm

current in 10 ohm, I = 50/20 = 2.5 A

power used by the resistor in middle = 2.5^2 * 10

power used by the resistor in middle = 62.5 W

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2)

time constant , T = 3 *10^3 * 5 *10^-6 s

T = 0.015 s

at t = 0.01 s

a) Voltage on the capacitor = Vo * (1 - e^(-t/T))

Voltage on the capacitor = 10 * (1 - e^(-0.01/.015))

Voltage on the capacitor = 4.87 V

b)

current in circuit = Io * e^(-t/T)

current in circuit = (10/3) * e^(-0.01/.015)
current in circuit = 1.711 mA

the current in circuit is 1.711 mA

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3)

distance of midpoint from wire , d = a/sqrt(3)

d = 10/sqrt(3) = 5.77 cm

as the magnetic field due to each wire is same and add up in the same direction

net field at the midpoint is given as

Bnet = 3 * u0 * I/(2 * pi * d)

Bnet = 3 * 4pi *10^-7 * 10/(2 * pi * 0.0577)

Bnet = 1.04 *10^-4 T

the magnetic field is 1.04 *10^-4 T INTO the plane