Electrical quantities：練習問題

What is the SI unit for electromotive force (e.m.f.)?

An electric motor is used to lift a weight. The motor operates at a potential difference of \(12\text{ V}\) and draws a current of \(2.0\text{ A}\). If the motor is used for \(1.0\text{ minute}\), how much electrical energy is transferred to the motor?

A battery with an electromotive force (e.m.f.) of \(E\) is used to move a charge \(Q\) around a complete circuit. In the same circuit, a potential difference (p.d.) of \(V\) exists across a specific resistor. Which row correctly describes the work done \(W\) by the source and the work done on the resistor?

A. Work done by source = \(EQ\); Work done on resistor = \(VQ\)
B. Work done by source = \(E/Q\); Work done on resistor = \(V/Q\)
C. Work done by source = \(VQ\); Work done on resistor = \(EQ\)
D. Work done by source = \(Q/E\); Work done on resistor = \(Q/V\)

Two identical metal spheres, A and B, are mounted on insulating stands. Sphere A has a charge of \( +8.0 \text{ nC} \) and sphere B is uncharged. They are brought into contact and then separated.

What is the final charge on sphere B and how many electrons were transferred during the process?

A lightning bolt transfers a charge of \(15\text{ C}\) to the ground in a time interval of \(0.50\text{ ms}\). What is the average current during the lightning strike?

Two copper wires, \( P \) and \( Q \), have the same length. Wire \( Q \) has a diameter that is twice the diameter of wire \( P \). If the resistance of wire \( P \) is \( 20\text{ }\Omega \), calculate the resistance of wire \( Q \).

A lightning bolt transfers a charge of \( 15 \text{ C} \) to the ground in a time interval of \( 2.5 \text{ ms} \). The potential difference between the cloud and the ground is \( 1.2 \times 10^{8} \text{ V} \). Calculate the average current during the strike and determine the total electrical energy transferred to the ground.

A metal wire has a resistance of \(15.0\text{ }\Omega\). If the wire is stretched uniformly until its length is tripled while its volume remains constant, calculate the new resistance of the wire.

A battery with an electromotive force (e.m.f.) of \(12\text{ V}\) is connected to a circuit consisting of a \(4.0\text{ }\Omega\) resistor in series with a parallel combination of two other resistors, \(R_1 = 6.0\text{ }\Omega\) and \(R_2 = 12.0\text{ }\Omega\). An ammeter is placed to measure the total current leaving the battery.

(a) Calculate the combined resistance of the parallel arrangement of \(R_1\) and \(R_2\).
(b) Determine the total resistance of the entire circuit.
(c) Calculate the reading on the ammeter.
(d) Determine the potential difference (p.d.) across the \(4.0\text{ }\Omega\) resistor.
(e) Calculate the current flowing specifically through the \(6.0\text{ }\Omega\) resistor.