Current Electricity Questions and Answers

Answer: C

The answer is Is excited.

A nerve fibre is excitable tissue. An electric current applied to it depolarises the membrane, and once the threshold is crossed an action potential, a nerve impulse, is set off, just as a natural stimulus would set it off. Electric stimulation is in fact the standard way of exciting nerves in physiology experiments.

The other options name particular behaviours (laughing, weeping) or the opposite effect (loss of sensation), none of which is the general response of nerve tissue to a current.

Answer: D

Specific resistance does not depend upon its length, mass and cross-section.

Resistance R of a wire is given by

\[ R = \rho \frac{l}{A} \]

where \(\rho\) is the specific resistance (resistivity). R changes with length and cross-sectional area, but \(\rho\) is a property of the material and its temperature only. Two copper wires of different sizes have different resistances but the same resistivity.

So the options saying it varies with length, cross-section or mass describe resistance, not specific resistance.

Answer: C

The steady state temperature is about 1986 °C.

The hot resistance is \(R_{2} = V/I = 230/2.3 = 100\ \Omega\). With \(R_{1} = 75\ \Omega\) at 25 °C and \(R_{2} = R_{1}[1 + \alpha(T_{2} - T_{1})]\):

\[ \begin{aligned} T_{2} - T_{1} &= \frac{R_{2} - R_{1}}{R_{1}\alpha} \\ &= \frac{100 - 75}{75 \times 1.7 \times 10^{-4}} \\ &\approx 1961\ ^{\circ}\text{C} \\ T_{2} &\approx 1961 + 25 = 1986\ ^{\circ}\text{C} \end{aligned} \]

1961 °C is the temperature rise only, before the room temperature of 25 °C is added back, which is the trap in this question. 1886 °C and 1925 °C come from arithmetic slips.

Answer: C

The internal resistance is 5 Ω.

The current through the 25 Ω external resistance follows from the terminal voltage, and the lost volts across the internal resistance from the difference between e.m.f. and terminal voltage:

\[ \begin{aligned} I &= \frac{1.25}{25} = 0.05\ \text{A} \\ r &= \frac{1.5 - 1.25}{0.05} = \frac{0.25}{0.05} = 5\ \Omega \end{aligned} \]

Equivalently, r = R(E/V - 1) = 25(1.5/1.25 - 1) = 5 Ω. Zero internal resistance would make the terminal voltage equal the e.m.f., and 25 Ω or 15 Ω would give much larger voltage drops.

Answer: C

The SI unit of current density is \(\text{Ampere/m}^{2}\).

Current density is the current flowing per unit cross-sectional area of a conductor:

\[ J = \frac{I}{A} \]

With current in amperes and area in square metres, its unit is the ampere per square metre. Ohm per square metre mixes resistance with area, coulomb per square metre is the unit of surface charge density, and ampere square metre is the unit of magnetic moment.

Answer: D

For resistances in parallel, \(\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}\).

In a parallel connection every resistor has the same voltage across it, and the total current is the sum of the branch currents:

\[ \begin{aligned} \frac{V}{R} &= \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}} \\ \frac{1}{R} &= \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} \end{aligned} \]

\(R = R_{1} + R_{2} + R_{3}\) is the rule for resistances in series. The version with 2 in every numerator has no basis, and multiplying the resistances gives the wrong unit.

Answer: B

The equivalent resistance is 10 ohm.

First combine the parallel pair, then add the series resistor:

\[ \begin{aligned} R_{p} &= \frac{10 \times 30}{10 + 30} = 7.5\ \Omega \\ R_{AB} &= 7.5 + 2.5 = 10\ \Omega \end{aligned} \]

12.5 ohm comes from adding 10 and 2.5 and ignoring the 30 ohm branch, and 30 ohm or 15 ohm come from treating the parallel pair wrongly. A quick check: two resistors in parallel always give less than the smaller of them, so the pair must be below 10 ohm.

Answer: D

Resistance does not depend on the applied potential difference.

For a wire at constant temperature, R = ρL/A: it depends on the length L, the cross-sectional area A and the resistivity ρ of the material. Increasing the potential difference increases the current in proportion (Ohm's law), but the ratio V/I, the resistance, stays the same.

Length, area and the nature of the material all appear in the formula, so they do affect resistance.

Answer: B

The phase wire is generally Red.

Under the colour code long followed in Indian house wiring, the phase (live) conductor is red, the neutral is black and the earth is green. In three-phase supplies the phases are red, yellow and blue.

Black is the neutral and green the earth under that code. Newer wiring standards follow international colours, in which blue is the neutral, so blue is not the general colour for a phase in house wiring either.

Answer: D

The resistance increases by 300%.

Stretching does not change the volume, so A × L stays constant: doubling the length halves the cross-section. With R = \(\rho L/A\):

\[ R' = \frac{\rho(2L)}{A/2} = 4R \]

The new resistance is four times the old, a change of (4R - R)/R = 300%. 100% comes from doubling the length but forgetting the thinner section, and 200% confuses 'four times' with 'increase of'.