Current Electricity Questions and Answers

Answer: E

The charge is 120 C.

Charge equals current multiplied by time, with the time in seconds.

\[ q = It = 2\ \text{A} \times 60\ \text{s} = 120\ \text{C} \]

The length of the wire does not matter. 2 C comes from taking the time as 1 s instead of 1 minute, and 60 C from forgetting the current of 2 A.

Answer: B

The resistivity is unchanged.

Resistivity is a property of the material, at a given temperature. It does not depend on the wire's length or thickness.

What changes is the resistance, R = ρL/A: halving L halves it, and doubling the radius makes A four times larger, so R falls to one eighth. The options halved, doubled, tripled and quadrupled confuse resistivity with resistance.

Answer: B

The key gives 12.2 Ω.

This value follows from the standard relation \(R_{t} = R_{0}(1 + \alpha t)\), with \(\alpha\) referred to 0 °C, applied at both temperatures:

\[ \begin{aligned} \frac{R_{80}}{R_{20}} &= \frac{1 + 4 \times 10^{-3} \times 80}{1 + 4 \times 10^{-3} \times 20} \\ &= \frac{1.32}{1.08} \approx 1.222 \\ R_{80} &\approx 12.2\ \Omega \end{aligned} \]

The quicker approximation \(R_{80} = R_{20}(1 + \alpha \times 60) = 12.4\ \Omega\) treats \(\alpha\) as referred to 20 °C and is not among the options. 1.22 and 2.44 Ω drop a factor of ten, and 24.4 and 38.8 Ω are far too large for a 60 °C rise.

Answer: C

The resistances are in the ratio 2 : 3 : 6.

The rate of flow of electrons is the current. Resistors in parallel share the same voltage, so \(I = \frac{V}{R}\) and \(R \propto \frac{1}{I}\).

\[ \begin{aligned} R_{1} : R_{2} : R_{3} &= \frac{1}{3} : \frac{1}{2} : 1 \\ &= 2 : 3 : 6 \end{aligned} \]

(multiplying through by 6). 6 : 3 : 2 is the inverse of the current ratio written the wrong way round, and 9 : 4 : 1 squares the current ratio.

Answer: D

The heat produced is in the ratio 1 : 2.

In series the same current flows through both resistors, so the heat in each, \(H = I^{2}Rt\), is proportional to its resistance.

\[ H_{2\Omega} : H_{4\Omega} = 2 : 4 = 1 : 2 \]

2 : 1 would apply if the resistors were in parallel, where the voltage is shared and \(H = \frac{V^{2}t}{R}\). The 12 V supply sets the size of the current but not the ratio.

Answer: B

The current is 0.5 A.

In the diagram the middle 4 V cell is reversed, so it opposes the other two. The net emf is

\[ \begin{aligned} \varepsilon &= 3 + 4 - 4 = 3 \text{ V} \\ R_{total} &= 0.5 + 0.75 + 0.75 + 4 = 6\ \Omega \\ I &= \frac{3}{6} = 0.5 \text{ A} \end{aligned} \]

Internal resistances add in series whatever the direction of each cell. If all three cells aided one another the current would be \(\frac{11}{6} \approx 1.8\) A, which is not offered.

Answer: C

The resistance is 12 Ω.

For the same material, \(R = \rho\frac{L}{A}\), so R is proportional to \(\frac{L}{A}\).

\[ \begin{aligned} R' &= 12 \times \frac{2}{1} \times \frac{0.1}{0.2} \\ &= 12\ \Omega \end{aligned} \]

Doubling the length doubles the resistance and doubling the area halves it, so the two effects cancel. 24 Ω and 6 Ω each apply only one of the two changes. Resistivity, the material property, is unchanged; only the dimensions alter the resistance.

Answer: D

The resistivity of both Cu and nichrome increases.

Copper and nichrome are metals (nichrome an alloy). Raising the temperature makes the lattice ions vibrate more, so electrons collide more often and resistivity rises; for nichrome the rise is small, which is why it is used in heating elements.

Germanium is a semiconductor. Heating frees more charge carriers, so its resistivity falls. Any option saying Ge's resistivity increases, or nichrome's decreases, is wrong.

Answer: B

The current is 0.67 A.

The two cells in parallel act as one cell of emf 2 V and internal resistance \(\frac{1}{2}\ \Omega\). In series with the third cell this gives 4 V and 1.5 Ω.

\[ I = \frac{4}{4.5 + 1.5} = \frac{4}{6} = 0.67\ \text{A} \]

Treating all three cells as in series gives \(\frac{6}{7.5} = 0.8\) A, and in parallel \(\frac{2}{4.83} \approx 0.41\) A; neither is offered.

Answer: B

The current increases heavily.

A short circuit occurs when the live and neutral wires touch directly, so the current bypasses the load. The resistance of the circuit becomes very small, and by Ohm's law, I = V/R, the current rises sharply. That is why fuses and circuit breakers are needed to cut the supply.

The current does not fall, stay the same or merely fluctuate; the sudden large rise is what makes a short circuit dangerous.