Series Circuits

Definition

Series connection is one in which → components → are connected 1 after another in a single loop

Circuits with components in series arrangements = series circuits

Since there is only one single loop → electric current has only one path to flow through.

Important

In a series circuit, current at every point is the same

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Potential Difference across a resistor is the work done per unit charge in driving the charges through that resister (Electromotive Force and Potential Difference) → thus there must be fall in electrical potential as the charge flows across $R_1$ and $R_2$ → these potential differences cannot be measured using voltmeter as shown. → the e.m.f of the cell E is equal to the sum of potential differences across $R_1$ and $R_2$

• voltage across source E = sum of $V_1$ and $V_2$

Important

In a series circuit, the total potential difference supplied to the circuit E is equal to the sum of the individual potential differences across the resistors.

Mathematically in reference to above figure:

$SinceV=IR$ $E=V_1+V_2$ $V_{\mathcal{E}}=I{R}_1+I{R}_2$ $R_1+R_2=\frac{V_{\mathcal{E}}}{I}$

We can define effective resistance $R_e$ such that $R_e=R_1+R_2=\frac{V}{I}$ hence circuit diagram in above figure can be replaced by equivalent circuit diagram below

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Formulae

In General → if there are n resistors connected in series, then: Since PD = IR $R_e=\frac{V_{\mathcal{E}}}{I}=R_1+R_2+....+R_n$

This means that when resistors are connected in series → they can be represented by an effective resistance of $R_e$

Important

In a series circuit, the effective resistance $R_e$ is equal to the sum of the individual resistances

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