Question

A p.d. of ${\text{4}}\,{\text{V}}$ is applied to two resistors of ${\text{6}}\,{\text{ohms}}$ and ${\text{2}}\,{\text{ohms}}$ connected in series. Calculate:
(a) the combined resistance
(b) the current flowing
(c) the p.d. across the ${\text{6}}\,{\text{ohms}}$ resistor

Answer 1

Hint:A resistor is a two-terminal passive electrical component that acts as a circuit element by implementing electrical resistance. Resistors are used in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active components.

Complete step by step answer:
When resistors are daisy chained together in a single line and a common current flows through them, they are said to be connected in series.
(a) Individual resistors in a series resistor network add up to give the series combination's equivalent resistance. A series circuit's resistors can be swapped out without affecting the total resistance, current, or power delivered to each resistor or the circuit.
We can calculate the combined resistance by
${{\text{R}}_{{\text{eq}}}}\,{\text{ = }}\,{{\text{R}}_{\text{1}}}\,{\text{ + }}\,{{\text{R}}_{\text{2}}} \\
\Rightarrow {{\text{R}}_{{\text{eq}}}}\,{\text{ = }}\,{\text{6}}\,\,{\text{ + }}\,\,{\text{2}} \\
\therefore {{\text{R}}_{{\text{eq}}}}\, {\text{ = }}\,{\text{8}}\,{\text{ohms}} \\ $
The combined resistance is ${\text{8}}\,{\text{ohms}}$.

(b) Resistors in series carry the same current, but their individual resistance values cause different voltage drops across each resistor, according to Ohm's Law $\left( {{\text{V}}\,{\text{ = }}\,{\text{IR}}} \right)$
p.d. applied to two ${\text{6}}\,{\text{ohm}}$ and ${\text{2}}\,{\text{ohm}}$resistors = \[{\text{4V}}\]
\[{\text{V}}\,{\text{ = }}\,{\text{IR}} \\
\Rightarrow {\text{I}}\,{\text{ = }}\,\dfrac{{\text{V}}}{{\text{R}}} \\
\Rightarrow {\text{I}}\,{\text{ = }}\,\dfrac{{\text{4}}}{{\text{8}}} \\
\therefore {\text{I}}\,{\text{ = }}\,{\text{0}}{\text{.5A}} \\ \]
The current flowing is ${\text{0}}{\text{.5A}}$.

(c) The potential difference across ${\text{6}}\,{\text{ohms}}\,\,\left( {{\text{r}}\,{\text{ = }}\,{\text{6}}\,{\text{ohms}}} \right)$ can be calculated as,
\[{\text{I}}\,{\text{ = }}\,\,{\text{0}}{\text{.5A}} \\
\Rightarrow{\text{V}}\,{\text{ = }}\,{\text{IR}} \\
\Rightarrow {\text{V}}\,{\text{ = }}\,{\text{0}}{{.5 \times 6}} \\
\therefore {\text{V}}\,{\text{ = }}\,{\text{3V}} \\ \]
Hence, the potential difference across ${\text{6}}\,{\text{ohms}}$ is ${\text{3V}}$.

Note:A series circuit's resistors can be swapped out without affecting the total resistance, current, or power delivered to each resistor or the circuit. Series resistors can be used to generate different voltages throughout themselves, and this form of resistor network is ideal for creating a voltage divider.