Which component has the \(I\)–\(V\) graph shown?
Correct Answer: \( \boxed{\mathrm{A}} \)
As the current increases, the filament becomes hotter, causing its resistance to increase.
The current therefore increases less rapidly with increasing voltage, giving a curve with a decreasing gradient.
Therefore, the correct answer is (A).
A piece of wire X has resistivity \(\rho\), length \(L\) and cross-sectional area \(A\). Wire X has a resistance \(R\).
A second piece of wire Y is made of a different metal. It has the same resistance as X but has twice the length of X.
Which row gives possible values for the resistivity and the cross-sectional area of Y?
| resistivity | cross-sectional area | |
|---|---|---|
| (A) | \(\dfrac{1}{2}\rho\) | \(\dfrac{1}{2}A\) |
| (B) | \(\dfrac{1}{2}\rho\) | \(A\) |
| (C) | \(\rho\) | \(\dfrac{1}{2}A\) |
| (D) | \(2\rho\) | \(A\) |
Correct Answer: \( \boxed{\mathrm{B}} \)
Resistance is given by \(R=\dfrac{\rho L}{A}\).
For wire Y, \(L\) doubles while the resistance remains unchanged.
Using \(\rho_Y=\dfrac{1}{2}\rho\) and \(A_Y=A\),
\(R_Y=\dfrac{\left(\frac{1}{2}\rho\right)(2L)}{A}=\dfrac{\rho L}{A}=R\).
Therefore, the correct answer is (B).
The graphs show possible current-voltage (\( I\!-\!V \)) characteristics for a filament lamp and for a semiconductor diode.
Which row identifies the \( I\!-\!V \) graphs for the lamp and for the diode?
| filament lamp | semiconductor diode | |
|---|---|---|
| A | P | R |
| B | P | S |
| C | Q | R |
| D | Q | S |
Correct Answer: \( \boxed{\mathrm{A}} \)
A filament lamp has a decreasing gradient on its \( I\!-\!V \) graph because its resistance increases as its temperature rises. This corresponds to graph \( P \).
A semiconductor diode conducts very little current until a threshold voltage is reached, after which the current increases rapidly. This corresponds to graph \( R \).
Therefore, the correct answer is (A).
