Combination Of Resistors Series And Parallel

When cells with identical emf and internal resistance are connected in parallel, the equivalent emf remains the same as the emf of a single cell because the emf values are the same for all cells. The equivalent internal resistance is given by the formula for resistances in parallel: Thus, Therefore, the equivalent emf is , and the equivalent resistance is .

We are given an equilateral triangle with each side having resistance . We need to find the effective resistance between two sides of the triangle.

1. Step 1: Visualize the resistances In an equilateral triangle, the three sides are identical, each with resistance . We are asked to find the effective resistance between two of the sides.

2. Step 2: Use the combination of resistors We can think of the triangle as having three resistors in a series and parallel combination. The resistance between the two chosen sides is equivalent to the parallel combination of two resistors: one from the chosen side directly to the third vertex, and the other from the other vertex to the third side.

3. Step 3: Apply the formula for parallel resistors The effective resistance between the two sides is the parallel combination of two resistors , which is given by: However, this must be done for all combinations of the sides, and the final result is: Thus, the effective resistance between two sides is .