B.5 Current and circuits：練習問題

According to Ohm's Law, an ohmic conductor is one where:

A cell has an electromotive force (emf) \( \epsilon \) and an internal resistance \( r \). It is connected to an external resistor of resistance \( R \). Which expression represents the ratio of the terminal potential difference to the emf of the cell?

A battery with an electromotive force (emf) of \( 12 \, \text{V} \) and an internal resistance of \( 2.0 \, \Omega \) is connected to a parallel combination of two external resistors with resistances of \( 3.0 \, \Omega \) and \( 6.0 \, \Omega \). What is the terminal potential difference across the battery when the circuit is closed?

Three resistors with values of \( 4.0 \, \Omega \), \( 6.0 \, \Omega \), and \( 10.0 \, \Omega \) are connected in series to a DC power supply with an electromotive force (emf) of \( 40 \, \text{V} \) and negligible internal resistance. What is the current flowing through the \( 6.0 \, \Omega \) resistor?

A cell with electromotive force \( \epsilon \) and internal resistance \( r \) is connected in series with a variable resistor of resistance \( R \). Which of the following statements correctly describes the changes in the terminal potential difference \( V \) across the cell and the electrical power \( P_{\text{int}} \) dissipated within the cell's internal resistance as the value of \( R \) is increased from a very low value?

A charge of \( 45 \text{ C} \) passes through a cross-section of a wire in a time interval of \( 1.5 \text{ minutes} \). Calculate the average electric current flowing through the wire.

A battery with an electromotive force (emf) of \( 12.0 \text{ V} \) and an internal resistance of \( 0.50 \, \Omega \) is connected to an external resistor of \( 5.5 \, \Omega \). Determine the terminal potential difference across the battery when the circuit is closed.

In a DC circuit consisting of two loops, Loop 1 contains a \( 12.0\text{ V} \) ideal battery and a \( 4.0\text{ }\Omega \) resistor, while Loop 2 contains a \( 9.0\text{ V} \) ideal battery and a \( 3.0\text{ }\Omega \) resistor. The two loops share a common central branch containing a \( 6.0\text{ }\Omega \) resistor; if both batteries have their positive terminals connected to the same top junction, calculate the current flowing through the central \( 6.0\text{ }\Omega \) resistor.

A simple DC circuit is constructed using a battery with an electromotive force (emf) of 12.0 V and an internal resistance of 2.0 \(\Omega\). This battery is connected in series with a fixed resistor of resistance 10.0 \(\Omega\).

(a) Calculate the total resistance of the circuit.
(b) Determine the current flowing through the circuit.
(c) Calculate the terminal potential difference across the battery when the circuit is closed.

(a) A battery with electromotive force (emf) \( \epsilon \) and internal resistance \( r \) is connected in series with a variable resistor \( R \). Show that the power dissipated in the external resistor \( R \) is given by \( P = \frac{\epsilon^2 R}{(R+r)^2} \).

(b) A student measures the potential difference across the battery terminals to be 9.0 V when the current is 1.5 A, and 8.0 V when the current is 2.5 A. Determine the emf and the internal resistance of the battery.