Electric Circuits Answers

A power transmission line is made of copper 1 .80cm in diameter. Find the resistance of one mile of this line.

Household wiring often contains 12-gauge copper wires, having a diameter of approx. 2 mm.

Consider a circuit of such a wire connecting a 60 W light-bulb with a standard 230 V household

outlet and a light switch 5 m away.

• What is the current drawn by the light bulb if you flick the switch?

• After what time t does the first electron from the voltage source reach the light bulb?

Assume the density of charge carriers to be n = 8 · 1028 m-3, and their charge to be

1e = 1.6·10-19 C. Does that time make sense, considering that the light bulb immediately

begins to shine, when flicking the switch?

• If i would want to collect 1 g of electrons from that wire in 1 hour, what current would

need to flow? (i.e. for 1 g of electrons passing the cross-section of the wire in 1 hour) The

mass of one electron is given as me = 9.1 · 10-31 kg.

• How big is the electric field in the copper wire, if we assume the wire to have a resistivity

ρ = 1.68 · 10-8 Ωm?

Design a combinational circuit with four inputs, w, x , y , and z , and four outputs, A, B , C and D. When the binary input is 0, 1, 2, or 3, the binary output is two greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the input. 

Let the enery stored "in the capacitor" be U. Show that U is given by the expression: U=½Q²/C

Rob has moved from North America to Australia, bringing most of his household effects including a portable room heater built for use in North America. The heater’s label says it is rated for 1500 W. He has planned to purchase a voltage conversion transformer so that he can operate these devices in his Australian home.

A. Explain how a transformer operates in general and how a transformer can be designed to convert input voltage to a different output voltage. (5 marks)

B. A friend proposes an inexpensive alternative to using a transformer. He says to go to purchase a standard Australian 2 prong plug from a hardware store, cut off the original plug from the heater’s cord and then connect the Australian plug to the wires of the cord. Explain why this approach is likely both a fire hazard and a shock hazard. (5 marks)

For a DC brush motor, if supply voltage = 200 V, Armature current = 10 Amp, and Armature resistance = 0.5 ohms, then the Eb will be …….

Points A and B are 0.10 m apart. A point charge of +3.0 x 10-9 C is placed at A and a

point charge of -1.0 x 10-9 C is placed at B.

I. X is the point on the straight line through A and B, between A and B, where the

electric potential is zero. Calculate the distance AX.

II. Show on a diagram the approximate position of a point, Y, on the straight line

through A and B where the electric field strength is zero.( no calculation is

expected)

Two light, conducting spheres, each 6 mm diameter and having a mass of 10 mg, are

suspended from the same point by fine insulated fibers of 50cm long. Due to electrostatic

repulsion the spheres are in equilibrium when 3 cm apart.

Points A and B are 0.10 m apart. A point charge of +3.0 x 10-9 C is placed at A and a

point charge of -1.0 x 10-9 C is placed at B.

I. X is the point on the straight line through A and B, between A and B, where the

electric potential is zero. Calculate the distance AX.

II. Show on a diagram the approximate position of a point, Y, on the straight line

through A and B where the electric field strength is zero.( no calculation is

expected)

What is the circuit (amps) for a series circuit containing a 12 V potential and three resistors R1= 3 ohms,

R2= 2 ohms and R3= 1 ohm.