D.C. Circuits：練習題

Three identical resistors, each with resistance \(R\), are connected such that two of them are in parallel with each other, and this parallel combination is then connected in series with the third resistor. What is the total effective resistance of this arrangement?

A circuit is powered by a cell of electromotive force ( ext{e.m.f.}) of \(6.0\text{ V}\) with negligible internal resistance. The cell is connected in series with a fixed resistor of resistance \(R_1 = 3.0\,\Omega\) and a parallel pair of identical resistors, each having a resistance of \(R = 6.0\,\Omega\).

What is the electrical power dissipated across the fixed resistor \(R_1\)?

In the diagram of a parallel circuit, there are two resistors with resistances \(R_1 = 4\,\Omega\) and \(R_2 = 12\,\Omega\) connected to a \(12\text{ V}\) battery. What is the total current flowing from the battery?

A circuit is set up with a variable resistor connected in series with a fixed resistor of \(10\,\Omega\) and a \(12\text{ V}\) power supply. If the variable resistor is adjusted from \(2\,\Omega\) to \(14\,\Omega\), what is the change in the power dissipated by the \(10\,\Omega\) fixed resistor?

A series circuit consists of a \(6\text{ V}\) battery, a \(2\,\Omega\) resistor, and a \(4\,\Omega\) resistor. What is the potential difference across the \(4\,\Omega\) resistor?

Two resistors, \( R_1 = 4 \, \Omega \) and \( R_2 = 6 \, \Omega \), are connected in series to a \( 12 \text{ V} \) battery. Calculate the total current flowing in the circuit.

Three identical resistors are connected in parallel. If the effective resistance of the combination is \( 2 \, \Omega \), determine the resistance of each individual resistor.

A circuit consists of a \( 12 \text{ V} \) power supply connected to a \( 3 \, \Omega \) resistor and a \( 6 \, \Omega \) resistor in parallel. This parallel combination is then connected in series with a \( 2 \, \Omega \) resistor. Calculate the total power dissipated by the entire circuit.

A student sets up a direct current (D.C.) circuit to investigate the properties of resistors. The circuit consists of a 12 V D.C. power supply connected in series with a switch and two resistors, \(R_1\) and \(R_2\).

(a) If \(R_1 = 4.0\) Ω and \(R_2 = 8.0\) Ω, calculate the effective resistance of the circuit when the switch is closed.
(b) Determine the current flowing through the circuit.
(c) Calculate the potential difference across resistor \(R_2\).