Resistances in Series

  • Recall and use R = V/I

  • Calculate the combined resistance of resistors connected in series.

  • Perform calculations on voltage divider circuits;

  • Define power as VI and apply the formula to calculate power dissipation in series circuits.

Components connected in series are only connected to each other at one point.
The same current flows through both components. The sum of the voltages across each component in the circuit equals the power supply voltage.

\[R_{\mathrm{series}} = R_1 + R_2 + R_3 + ......................\]

Series Direct Current Circuit Rules:

  1. The same current flows through each part of a series circuit.

  2. Total Resistance of a series circuit is equal to the sum of the individual resistances.

  3. The total voltage across a series circuit is equal to the sum of the individual voltage drops.

  4. The voltage drop across a resistor in a series circuit is proportional to the size of the resistor.

  5. The total power dissipated in a series circuit is equal to the sum of the individual power dissipation.

Solved Example:

19-3-01

If length of a conductor is doubled by keeping volume constant, then what is its new resistance if initial were 4 $\Omega$ ?

Correct Answer: D

Solved Example:

19-3-02

A cell of e.m.f 2 V and internal resistance 0.5 $\Omega$ is connected across a resistor R. The current that flows is same as that, when a cell of e.m.f 1.5 V and internal resistance 0.3 $\Omega$ is connected across the same resistor. Then:

Solution:
\begin{align*} \dfrac{2}{0.5 + R} &= \dfrac{1.5}{0.3 + R}\\ R &= 0.3\ \Omega \end{align*}

Correct Answer: A