Question

Q. Calculate the net resistance of a circuit having
three 6Ω resistors connected in parallel with
each other and then in series with a 9Ω
resistor?​

Answer 1

Answer:-

• Three resistors of 6 ohm are connected in parallel.
• One resistor of 9 ohm is connected in series.

Finding the net resistance in the parallel connection:-

$\mapsto\green{\tt{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}=\dfrac{1}{R_{p}}}}$

$\mapsto\tt{\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{1}{R_{p}}}$

$\mapsto\tt{\dfrac{1}{R_{p}}=\dfrac{1+1+1}{6}}$

$\mapsto\tt{\dfrac{1}{R_{p}}=\cancel{\dfrac{3}{6}}}$

$\mapsto\tt{\dfrac{1}{R_{p}}=\dfrac{1}{2}}$

$\mapsto\purple{\tt{R_{p}=2\:\Omega}}$

Finding the total resistance in the circuit:- The resistance in the parallel circuit + The resistance in the series circuit.

$\mapsto{\tt{R_{n}=2\:\Omega + 9\:\Omega}}$

$\mapsto\pink{\tt{R_{n}=11\:\Omega}}$

$\rule{200}1$

• If the parallel resistance is to be calculated, its reciprocal is added to find the total parallel resistance.
• If resistance in a series circuit is to be calculated, it can be directly added.

$\rule{200}2$

Answer 2

$\large \underline{ \red{ \boxed{ \bf \orange{Required \: Answer}}}}$