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?

# Challenge Problems

# 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.

# A block and a triangular wedge move together

A block of mass m and a triangular wedge of mass M move together without slipping due to a pulling force F. The triangular wedge has a slope α. There is no friction between any pair of surfaces. Derive an equation of pulling force.

# A system of three objects

A system is composed of three objects with masses m, 5m and 6m. The coefficient of kinetic friction between the objects m, 5m and the surface is 0.5. Find the acceleration of the objects.

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# Magnetic field due to a current in a straight wire

A corner point makes angles θ_{1} and θ_{2} with the ends of a straight wire carrying current I. The distance of the point from the wire is a. What is the

magnetic field at the point?

# The boat is pulled to the shore

A boy stands on a shore and pulls a rope connected to a boat. The velocity of the rope v_{r} is constant. Prove that the closer the boat to the shore, the faster it moves.