Ohms Law and Resistance - UNSOLVED PRACTICE SET

Q7. State Ohm's Law. Under what conditions is it valid?

Q8. A wire of resistance 10 Ω is drawn out to triple its original length. Calculate its new resistance.

Q9. Why does the resistance of a conductor increase with temperature? Explain at the atomic level.

Q10. Draw the V-I characteristics for (a) an ohmic conductor, and (b) a non-ohmic conductor (like a diode). Label them clearly.

Q11. A wire of resistance R is cut into two equal parts and connected in parallel. What is the equivalent resistance?

Q12. The resistance of a wire is 4 Ω. If its radius is doubled and its length is halved, what is the new resistance?

Q13. State and explain Ohm's Law. Derive the expression for the resistance of a conductor in terms of its resistivity, length, and cross-sectional area. Explain why resistance is called a "property" of the conductor.

Q14. Explain the difference between ohmic and non-ohmic conductors. Give two examples of each. Why does a light bulb (tungsten filament) not strictly obey Ohm's Law?

Q15. In a school experiment, a student plots the V-I characteristics of a resistor and obtains a straight line passing through the origin with slope 0.5 A/V.

(a) What is the resistance of the resistor?

(b) If the potential difference across the resistor is 6 V, what is the current through it?

(c) Calculate the power dissipated in the resistor at this voltage.

(d) If the resistor is replaced by a semiconductor diode, how would the V-I graph change? Sketch it roughly.

Q16. A copper wire has length l = 5 m and cross-sectional area A = 2 × 10⁻⁶ m². The resistivity of copper is ρ = 1.7 × 10⁻⁸ Ω m.

(a) Calculate the resistance of the wire.

(b) If a potential difference of 12 V is applied across the wire, calculate the current flowing through it.

(c) Calculate the power dissipated as heat in the wire.

(d) The wire is now stretched uniformly to double its length. Calculate the new resistance and the new current for the same 12 V potential difference.

Q17. In your home, the wiring for a 100 W bulb uses copper wire of diameter 0.5 mm. The length of the wire from the switch to the bulb is 10 m.

(a) Calculate the resistance of the copper wire. [Given: ρ = 1.7 × 10⁻⁸ Ω m]

(b) If the bulb operates at 220 V, calculate the current drawn by the bulb.

(c) Calculate the potential drop across the connecting wire. Is this significant compared to 220 V?

(d) If the wire were made of aluminium (ρ = 2.8 × 10⁻⁸ Ω m) of the same dimensions, how would the potential drop change?

Q18. A wire of resistance 36 Ω is bent into the shape of a square.

(a) Calculate the resistance between two opposite corners of the square.

(b) Calculate the resistance between two adjacent corners of the square.

(c) If the same wire is bent into a circle, what is the resistance between two points on the diameter?

(d) A student claims that the resistance in part (a) should be 18 Ω because the wire is divided into two equal parts. Explain why this reasoning is incorrect.