Question

Three resistances of 4 ohms, 6 ohms and 10 ohms are connected in series. The potential difference across the combination is 5 V. Calculate the potential difference across each resistor.

Answer 1

Concept used: Series combination of resistance

Step 1: Given Data,

Potential difference across the combination $=5\mathrm{V}$

Three resistances are connected in series,

$$\begin{gathered} {\mathrm{R}}_1=4\mathrm{\Omega } \\ {\mathrm{R}}_2=6\mathrm{\Omega } \\ {\mathrm{R}}_3=10\mathrm{\Omega } \end{gathered}$$

Step 2: Finding the equivalent resistance,

Consider ${\mathrm{R}}_1,{\mathrm{R}}_2,{\mathrm{R}}_3$ are the three resistance are connected in series,

The equivalent resistance of a circuit connected in series is equal to the sum of their individual resistances.

Hence equivalent resistance is

$$\begin{gathered} \mathrm{R}={\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{R}}_3 \\ =4+6+10 \\ \mathrm{R}=20\mathrm{\Omega } \end{gathered}$$

Step 3: Finding the current through the circuit,

In a series combination, the current passing through each resistance is the same.

By Ohm's law,

$$\begin{gathered} \mathrm{Current}\mathrm{I}=\frac{\mathrm{Potential}\mathrm{difference}\mathrm{V}}{\mathrm{Resistance}\mathrm{R}} \\ =\frac{5}{20} \\ \mathrm{Current}\mathrm{I}=0.25\mathrm{A} \end{gathered}$$

Step 4: Finding the voltage through each resistance,

The potential difference across $4\mathrm{\Omega }$ resistor,

$$\begin{gathered} {\mathrm{V}}_1=\mathrm{I}\times {\mathrm{R}}_1 \\ =0.25\times 4 \end{gathered}$$

The potential difference across $4\mathrm{\Omega }$ resistor ${\mathrm{V}}_1=1\mathrm{\Omega }$.

The potential difference across $5\mathrm{\Omega }$ resistor,

$$\begin{gathered} {\mathrm{V}}_2=\mathrm{I}\times {\mathrm{R}}_2 \\ =0.25\times 6 \end{gathered}$$

The potential difference across $6\mathrm{\Omega }$ resistor is ${\mathrm{V}}_2=1.5\mathrm{\Omega }$.

The potential difference across $10\mathrm{\Omega }$ resistor,

$$\begin{gathered} {\mathrm{V}}_3=\mathrm{I}\times {\mathrm{R}}_3 \\ =0.25\times 10 \end{gathered}$$

Potential Difference across $10\mathrm{\Omega }$ resistor,${\mathrm{V}}_3=2.5\mathrm{\Omega }$.