Calculate the combined e.m.f. of several sources in series

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IGCSE Physics - Series and Parallel Circuits - Combined e.m.f.

IGCSE Physics - 4.3.2 Series and Parallel Circuits

Objective: Calculate the combined e.m.f. of several sources in series

Introduction

In electrical circuits, voltage is provided by sources such as batteries. When multiple voltage sources are connected in series, their voltages add up. This combined voltage is known as the combined electromotive force (e.m.f.). This section will explain how to calculate the combined e.m.f. of multiple sources in series.

Series Circuits

In a series circuit, components are connected one after the other, forming a single path for the current. The current through each component is the same. When voltage sources are connected in series, the total voltage is the algebraic sum of the individual e.m.f. values.

Calculating Combined e.m.f. in Series

When $n$ voltage sources are connected in series, the total e.m.f. ($V_{total}$) is calculated by adding the e.m.f. of each individual source:

$$V_{total} = V_1 + V_2 + V_3 + ... + V_n$$

Where:

  • $V_1, V_2, V_3, ..., V_n$ are the e.m.f. values of the individual voltage sources.

Example Calculation

Consider three batteries connected in series. The e.m.f. values of these batteries are 9V, 12V, and 18V respectively. Calculate the total e.m.f. of the series combination.

  1. Identify the e.m.f. values of each battery: $V_1 = 9V$, $V_2 = 12V$, $V_3 = 18V$.
  2. Apply the formula for combined e.m.f. in series:
  3. $$V_{total} = V_1 + V_2 + V_3$$ $$V_{total} = 9V + 12V + 18V$$ $$V_{total} = 39V$$

Therefore, the total e.m.f. of the series combination is 39V.

Table Summary

Concept Description
Series Circuit Components connected end-to-end, providing a single path for current.
Combined e.m.f. (Series) The total voltage produced when multiple voltage sources are connected in series. Calculated by adding the individual e.m.f. values.
Formula (Series) $$V_{total} = V_1 + V_2 + V_3 + ... + V_n$$

Important Note

When voltage sources are connected in series, the total e.m.f. is the sum of the individual e.m.f. values. The polarity of the voltage sources must be considered to ensure correct addition.