Free Resistance and Resistivity MCQs with Answers

1. The resistance of a uniform wire is

• A. proportional to its length and to its cross sectional area
• B. proportional to its length and inversely proportional to its cross sectional area
• C. independent of its dimensions
• D. inversely proportional to its length

Explanation: R equals rho L over A, so a longer wire offers more resistance and a thicker one less, which is why thick cables are used for heavy currents. The constant rho is the resistivity, a property of the material rather than of the sample. Doubling the diameter quarters the resistance, because area depends on the square of the radius.

2. A wire is stretched so that its length doubles while its volume stays constant. Its resistance becomes

• A. double
• B. half
• C. four times
• D. unchanged

Explanation: Constant volume means doubling the length halves the cross sectional area, and since resistance is proportional to length over area, the effect is two multiplied by two, giving four times the original. Answering double accounts for the length change only. This is a favourite examination trick precisely because the area change is easy to overlook.

3. The SI unit of resistivity is

• A. ohm
• B. ohm metre
• C. ohm per metre
• D. volt per ampere

Explanation: Rearranging R equals rho L over A gives rho equal to RA over L, whose units are ohm times metre squared divided by metre, that is ohm metre. The plain ohm, equivalently the volt per ampere, is the unit of resistance itself. Resistivity is a material property, so copper has the same resistivity whether it is a thin wire or a thick bar.

4. Three resistors of 2, 3 and 5 ohms are connected in series. The total resistance is

• A. 10 ohms
• B. 0.97 ohms
• C. 1.03 ohms
• D. 30 ohms

Explanation: Series resistances simply add, giving 10 ohms, and the same current passes through each while the voltages divide in proportion to the resistances. In parallel the reciprocals add, which for these values gives about 0.97 ohms, always less than the smallest resistor. Recognising which arrangement the question describes is half the work.

5. Two 6 ohm resistors are connected in parallel. Their combined resistance is

• A. 12 ohms
• B. 6 ohms
• C. 3 ohms
• D. 0.33 ohms

Explanation: For two equal resistors in parallel the result is simply half of one of them, so 3 ohms. The general rule is that the reciprocals add, and the total is always smaller than the smallest branch because the current has more than one path available. Adding to get 12 ohms is the series answer.

6. The reciprocal of the resistivity of a material is called its:

• A. Impedance
• B. Conductivity
• C. Admittance
• D. Reactance

Explanation: Conductivity measures how readily a material carries current and is the reciprocal of resistivity, with units of siemens per metre. Admittance is the reciprocal of impedance and reactance is the opposition offered by a capacitor or inductor, both of which belong to circuit analysis rather than to material properties. Copper has a high conductivity and rubber a very low one.

7. If the length of the conductor is made 4 times its original length, its resistance becomes

• A. Quarter
• B. Half
• C. Zero
• D. 4 times

Explanation: Resistance is proportional to length for a given cross section and material, so quadrupling the length quadruples the resistance. Note that if the wire were stretched to four times its length at constant volume, the area would fall to a quarter and the resistance would rise sixteenfold, which is the harder variant of this question. Here only the length is stated to change.