A circular coil of wire, with N turns of radius a, is located in the field of an electromagnet. The magnetic field is perpendicular to the coil (that is, parallel to the axis of the coil) and its strength has the constant value B, over that area. The coil is connectd by a pari of twisted leads to an exteranl resistance. The toal resistance of this closed circuit, including that of the coil itself, is R. Suppose the electromagnet is turned off, its field dropping rapidly to zero. The induced electromotive force causes current to flow around the circuit. Derive a formula for the total charge Q = Sidt that passes through the resistor and explain why it does not depend on the rapidity with which the field drops to zero.

Avoltage source vs = 10 v is in series with a resistor of 10 kohm. if the source transformation theorem is applied, what will the value of the current source be in ma ?

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

Apiece of metal 75g at 110°c is dropped in a container with 500g at 20°c. the h2o if temperature is 24°c find specific heat capacity of metal