Consider the following part of an electric circuit: The total electrical resistance in the given part of the electric circuit is
15/7 ohm
Concept-
Obstruction offered to the flow of current is known as resistance. When two resistors are connected in series then the equivalent resistance is Rser = R 1+ R 2
When two resistors are connected in parallel then the equivalent resistance is
\(\frac{1}{{{R}_{para}}}=~\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}\)
Explanation-
From the above figure it is very much clear that 2 Ω, 4 Ω and 8 Ω are in parallel combination.
∴ Equivalent resistance is
\(\frac{1}{{{R}_{para}}}=~\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}\)
\(\frac{1}{{{R_{para}}}} = \;\frac{1}{{2{\rm{\;\Omega }}}} + \frac{1}{{4{\rm{\;\Omega }}}} + \frac{1}{{8{\rm{\;\Omega }}}} = \;\frac{{4 + 2 + 1}}{8} = \frac{7}{8}\)
\({R_{para}} = \frac{8}{7}{\rm{\Omega }}\)
From above figure it is very clear that 8/7 Ω and 1 Ω are in series.
∴ Rser = R 1+ R 2
\({R_{ser}} = \frac{8}{7} + 1 = \frac{{8 + 7}}{7} = \frac{{15}}{7}{\rm{\Omega }}\)
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