Electricity | Class 10 Science Notes

11.6 RESISTANCE OF A SYSTEM OF RESISTORS

Resistors can be connected in two main ways in electric circuits: in series and in parallel. Understanding how their equivalent resistance behaves is essential for circuit analysis.

In series connection, resistors are connected end to end so that the same current flows through each resistor. The total potential difference across the combination is the sum of the potential differences across individual resistors. The equivalent resistance R_s of resistors R_1, R_2, and R_3 connected in series is given by R_s = R_1 + R_2 + R_3.

In parallel connection, resistors are connected such that their ends are connected to the same two points, and the potential difference across each resistor is the same. The total current in the circuit is the sum of the currents through each resistor. The reciprocal of the equivalent resistance R_p of resistors R_1, R_2, and R_3 connected in parallel is given by 1/R_p = 1/R_1 + 1/R_2 + 1/R_3.

Activities demonstrate these properties by measuring currents and voltages in series and parallel resistor combinations.

Examples illustrate calculations of total resistance, current, and potential difference in circuits with series and parallel resistors.

This section provides the fundamental rules for combining resistors in circuits, enabling the analysis and design of complex electrical systems.

📊 Diagram: Figure 11.6 Resistors in series; Figure 11.7 Resistors in parallel; Figure 11.8 showing voltmeter connections across series resistors; Figure 11.9 An electric lamp connected in series with a resistor of 4Ω to a 6V battery; Figure 11.10 and 11.11 showing parallel resistor circuits; Figure 11.12 An electric circuit showing the combination of series and parallel resistors.

🧪 Activity: Activity 11.4: Connect resistors in series; measure current and voltage; verify current constancy and voltage addition. Activity 11.5: Measure voltage across series resistors. Activity 11.6: Connect resistors in parallel; measure currents and voltages; verify current division and voltage equality.

🔗 Connection: This section leads to the heating effect of electric current and its applications.