Circuits and Domestic Electricity：練習問題

An electric appliance is marked with the rating "\(220\,\text{V}, 1100\,\text{W}\)". What is the operating current of this appliance when it is connected to a \(220\,\text{V}\) mains supply?

Three resistors, each of resistance \(6\,\Omega\), are connected in a circuit. Two of the resistors are connected in parallel, and this parallel combination is then connected in series with the third resistor. If this arrangement is connected across a \(9\,\text{V}\) ideal power supply, what is the current flowing through the resistor that is connected in series?

A battery with electromotive force (e.m.f.) \(E\) and internal resistance \(r\) is connected to a load resistor of resistance \(R = 2r\). A voltmeter of internal resistance \(R_V = 6r\) is then connected in parallel with the load resistor. What is the ratio of the reading of the voltmeter to the initial terminal voltage of the battery (before the voltmeter was connected)?

If a charge of \(45\,\text{C}\) passes through a point in an electrical circuit in \(9\,\text{s}\), what is the average current flowing through that point?

Two cylindrical heating elements, X and Y, are made of the same alloy. Element X has a length \(l\) and a radius \(r\), while element Y has a length \(2l\) and a radius \(2r\). If both elements are connected in parallel across a constant voltage mains supply, what is the ratio of the power dissipated by X to the power dissipated by Y?

A circuit consists of a battery with an e.m.f. of $$9.0\,\text{V}$$ and an internal resistance of $$1.0\,\Omega$$. It is connected to an external resistor of $$8.0\,\Omega$$. Calculate the power dissipated by the external resistor.

A battery has an e.m.f. of $$10.0\,\text{V}$$ and an internal resistance of $$2.0\,\Omega$$. An external resistor $$R$$ is connected across its terminals. If the power dissipated in the external resistor is $$8.0\,\text{W}$$, what is the value of $$R$$?

An electric heater is rated "$$240\,\text{V}, 2400\,\text{W}". It is connected to a mains supply with an e.m.f. of$$240\,\(\text{V}\)$$through an extension cord with a total resistance of$$1.5\,\Omega$$. Calculate the actual power dissipated by the heater when in use.

A television has a power rating of 120 W and is connected to a 220 V domestic mains supply.

(a) Calculate the operating current of the television.

(b) If the television is switched on for an average of 5 hours per day, calculate the energy consumed by the television in kilowatt-hour (kWh) in one day.

An emergency lighting system is powered by a battery with an e.m.f. of \(12.0\text{ V}\) and an internal resistance of \(0.5\text{ }\Omega\). The system consists of three identical lamps connected in parallel across the battery. Each lamp has a power rating of "\(12.0\text{ V}, 6.0\text{ W}\)".

(a) Calculate the resistance of each lamp when it is operating at its rated voltage.

(b) Determine the terminal voltage of the battery when all three lamps are switched on simultaneously.

(c) If one of the lamps burns out and becomes an open circuit, explain how the brightness of the remaining two lamps would change. Assume the resistance of the lamps remains constant.