Circuits：練習問題

Three resistors with resistances \( R_1 = 10 \text{ } \Omega \), \( R_2 = 20 \text{ } \Omega \), and \( R_3 = 30 \text{ } \Omega \) are connected in series. What is the total resistance of the combination?

A \( 12 \text{ V} \) battery is connected to two resistors in parallel. One resistor has a resistance of \( 6.0 \text{ } \Omega \) and the other has a resistance of \( 12.0 \text{ } \Omega \). What is the total current drawn from the battery?

Consider a circuit with a \( 24 \text{ V} \) supply. Resistors \( R_1 = 4.0 \text{ } \Omega \) and \( R_2 = 8.0 \text{ } \Omega \) are connected in series. This series combination is then connected in parallel with a third resistor \( R_3 = 12.0 \text{ } \Omega \). What is the current flowing through \( R_1 \)?

Two resistors, \(4 \, \Omega\) and \(6 \, \Omega\), are connected in parallel. Calculate their equivalent resistance.

A circuit contains three identical resistors, each with resistance \(R\). Two are connected in parallel, and this combination is then connected in series with the third resistor. If the total equivalent resistance of the circuit is \(10 \, \Omega\), calculate the value of \(R\).

A circuit consists of a \(12 \, \text{V}\) power supply connected to two resistors in series, \(R_1 = 4.0 \, \Omega\) and \(R_2 = 8.0 \, \Omega\). This series combination is then connected in parallel with a third resistor, \(R_3 = 6.0 \, \Omega\).
(a) Calculate the total resistance of the circuit.
(b) Determine the total current drawn from the power supply.

Consider the circuit shown below. A \(24 \, \text{V}\) power supply is connected to a circuit with resistors \(R_1 = 10 \, \Omega\), \(R_2 = 15 \, \Omega\), and \(R_3 = 20 \, \Omega\). \(R_1\) is in series with a parallel combination of \(R_2\) and \(R_3\).
(a) Calculate the equivalent resistance of the parallel combination of \(R_2\) and \(R_3\).
(b) Determine the total resistance of the entire circuit.
(c) Calculate the total current drawn from the power supply.
(d) Find the current flowing through resistor \(R_2\).
(e) Calculate the power dissipated in resistor \(R_1\).