Current Electricity

Current Electricity deals with charges in motion, the steady currents that run every electrical device, from a torch to a power grid. In this chapter you will learn the meaning of electric current, how free electrons in a metal drift under an electric field, and how the current is related to drift velocity by I = neAvd. You will derive Ohm's law from this picture, define resistivity, conductivity and mobility, and see how the resistivity of metals, semiconductors and alloys changes with temperature. You will also learn the limitations of Ohm's law with examples of non-ohmic devices. You will study electrical energy and power, the emf and internal resistance of a cell, and the difference between emf and terminal voltage. The chapter explains combinations of resistors and of cells in series and parallel. You will apply Kirchhoff's junction rule, based on conservation of charge, and loop rule, based on conservation of energy, to solve circuits, and derive the balance condition of the Wheatstone bridge.

Detailed Worksheet: Current Electricity Section A - Definitions (10 marks) 1. Define drift velocity and relaxation time of free electrons in a conductor. (2 marks) 2. Define resistivity. On what factors does it depend? Write its SI unit. (2 marks) 3. Define mobility of charge carriers and write its SI unit. (2 marks) 4. Distinguish between the emf of a cell and its terminal voltage. (2 marks) 5. State Kirchhoff's junction rule and loop rule, naming the conservation law behind each. (2 marks) Section B - Calculations and Applications (15 marks) 6. A copper wire of cross-sectional area 1.0 x 10^-7 m^2 carries a current of 1.5 A. The number density of free electrons is 8.5 x 10^28 m^-3. Calculate the drift velocity (e = 1.6 x 10^-19 C). (3 marks) 7. A wire of resistivity 1.7 x 10^-8 ohm m has length 10 m and cross-sectional area 1.0 x 10^-6 m^2. Find its resistance. If the wire is stretched to double its length, find its new resistance. (3 marks) 8. A silver wire has a resistance of 2.1 ohm at 27.5 degree C and 2.7 ohm at 100 degree C. Find the temperature coefficient of resistivity of silver. (3 marks) 9. A battery of emf 10 V and internal resistance 3 ohm is connected to a resistor. The current in the circuit is 0.5 A. Find the resistance of the resistor and the terminal voltage of the battery. (3 marks) 10. A 2 ohm resistor is connected in series with a parallel combination of 3 ohm and 6 ohm resistors, across a 12 V battery of negligible internal resistance. Find the equivalent resistance, the current through each resistor and the power dissipated in the 2 ohm resistor. (3 marks) Section C - Diagrams (10 marks) 11. Draw a circuit diagram of a Wheatstone bridge and derive the balance condition P/Q = R/S using Kirchhoff's rules. (4 marks) 12. Draw graphs of resistivity against temperature for (i) copper, (ii) nichrome and (iii) a semiconductor, and explain their shapes. (3 marks) 13. Draw the I-V graph of an ohmic conductor and of a non-ohmic device such as a diode. State two ways in which Ohm's law can fail. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A cell of emf 6 V in series with a 2 ohm resistor and another cell of emf 4 V in series with a 4 ohm resistor are connected in parallel (positive terminals together) across a 4 ohm load. Using Kirchhoff's rules, find the current in each branch and in the load. Explain why one branch carries no current. (5 marks) 15. In a Wheatstone bridge, P = 10 ohm, Q = 20 ohm and R = 15 ohm. Find the value of S for balance. With S at this value and a 6 V battery across the bridge, find the current drawn from the battery. Explain why the galvanometer branch can be ignored at balance. (5 marks) 16. n identical cells, each of emf E and internal resistance r, are connected (i) in series and (ii) in parallel to an external resistance R. Derive the current in each case. When is each arrangement preferable? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Draw circuit diagrams, mark current directions and show units at every step.