A student built an electric circuit that consists of an ideal battery, a voltmeter with resistance R_{V}, an ammeter with resistance R_{A} and a resistor R. She connected all elements in the circuit as shown in Fig. (1). The voltmeter showed a reading of 1V and the ammeter showed a current of 1A. Then, another student switched between the voltmeter and ammeter Fig. (2). As a result, the voltmeter showed the reading of 2V and the ammeter showed the current of 0.5A. What is the resistance of the resistor?

# Author: Boris Sapozhnikov

# STAR connection

Three batteries have their negative terminals connected together.

Find the voltage read by an ideal voltmeter.

# A rod carries a charge uniformly distributed along its length

A rod of length L carries a charge Q uniformly distributed along its length.

Find the electrical field at point P on the axis of the rod, a distance a away from the end of the rod.

# The rod is “flying” above the cable

A conducting rod of length l, mass m, and resistance R is suspended by two vertical conducting wires of lengths d each. The circuit consists of a battery ε, the horizontal fixed wires, two parallel vertical wires , and the conducting rod. All conducting wires have negligible resistance and mass. There is a conducting long cable. The cable is below the rod and at a distance x.

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# The equation of radioactive decay

The half-life of Molybdenum-93 is 4000 years. A sample of Molybdenum-93 has a mass of 10 mg. When will the mass be reduced to 1 mg?

Image Source: Virtual museum of chemical elements.

# A ball is attached to a string and swung so that it travels in a horizontal circle

A ball of mass 0.2 kg is attached to a massless string 1 m long and swung so that it travels in a horizontal circle of radius 0.5 m.

a) Draw a free-body diagram.

b) Find the force of tension in the string as the ball swings in a horizontal circle.

c) Find the period of the ball’s motion.

# The quantum tunneling phenomenon

The quantum tunneling phenomenon is negligible in the classical mechanics.

Show that the tunneling probability equals 0 for an object of mass 0.007 kg moving at a speed of 0.1 m/s against a solid obstacle of height 0.05 m and width 0.01 m.