電動勢與內電阻：練習題

A cell has an electromotive force (emf) of \( \mathcal{E} \) and an internal resistance \( r \). When connected to an external circuit, it delivers a current \( I \). Which of the following statements correctly describes the terminal potential difference \( V \) across the cell?

A power supply has an EMF of \( 12.0 \text{ V} \) and an internal resistance of \( 0.50 \text{ } \Omega \). It is connected to an external resistor of resistance \( R \). If the current flowing through the circuit is \( 2.0 \text{ A} \), what is the terminal potential difference across the power supply?

A cell with EMF \( 1.5 \text{ V} \) and internal resistance \( 0.20 \text{ } \Omega \) is connected in series with a \( 2.8 \text{ } \Omega \) resistor and a parallel combination of two resistors, \( 4.0 \text{ } \Omega \) and \( 6.0 \text{ } \Omega \). Calculate the current flowing through the \( 4.0 \text{ } \Omega \) resistor.

The graph shows the terminal potential difference \( V \) across a cell varying with the current \( I \) supplied by the cell.
The line intercepts the V-axis at \( 6.0 \text{ V} \) and the I-axis at \( 3.0 \text{ A} \). What are the EMF and internal resistance of the cell?

A cell has an EMF of \(1.5 \, V\) and an internal resistance of \(0.5 \, \Omega\). When it is connected to an external resistor, the terminal potential difference is \(1.2 \, V\). Calculate the current flowing through the circuit and the resistance of the external resistor.

A student investigates the terminal potential difference (PD) of a cell as the current drawn from it varies. The following data are collected:

Current \(I\) / A | Terminal PD \(V\) / V
---|---
0.10 | 1.45
0.20 | 1.40
0.30 | 1.35
0.40 | 1.30
0.50 | 1.25

(a) On a piece of graph paper, plot a graph of terminal PD \(V\) (y-axis) against current \(I\) (x-axis). Draw a best-fit straight line.
(b) Use your graph to determine the electromotive force (emf) of the cell.
(c) Use your graph to determine the internal resistance of the cell.
(d) Explain why the terminal PD decreases as the current increases.

A cell has an electromotive force (emf) of \(1.5 \, \text{V}\) and an internal resistance of \(0.50 \, \Omega\). It is connected to an external resistor \(R_L = 2.5 \, \Omega\).
(a) Calculate the current flowing through the circuit.
(b) Determine the terminal potential difference (PD) across the external resistor.
(c) Calculate the power dissipated by the internal resistance of the cell.
(d) If a second identical external resistor of \(2.5 \, \Omega\) is connected in parallel with the first external resistor, calculate the new current drawn from the cell.