Question

two resistors of resistance 6 ohm and 3 ohm are connected in series and then in parallel .calculate the equivalent series resistance and equivalent parallel resistance.​

Answer 1

Answer:

a. RT = 9 Ohms

b. RT = 0.5 Ohms

Explanation:

Let the two resistors be A and B.

Let RT be equivalent resistance.

Given the following data;

Resistor A = 6ohms

Resistor B = 3ohms

a. To find the equivalent series resistance;

RT = RA + RB

RT = 6 + 3

RT = 9 Ohms

b. To find the equivalent parallel resistance;

RT = 1/RA + 1/RB

Substituting into the equation, we have

RT = 1/6 + 1/3

RT = 3/6

RT = 0.5 Ohms

Answer 2

As here the 6 ohm and 3 ohm resistors are first connected in series and then parallel, so we can just find out the equivalent series resistance by the formula of it, which is the individual sum of all resistors (for series) and for parallel combination, the reciprocal of the total resistance is the individual reciprocal sum of all resistors, so if we apply same Formula here for series first, then we will be having :

${:\implies \quad \sf R_{s}=6+3}$

${:\implies \quad \boxed{\bf{R_{s}=9\Omega}}}$

Now, for parallel combination:

${:\implies \quad \sf \dfrac{1}{R_{p}}=\dfrac13 +\dfrac16}$

${:\implies \quad \sf \dfrac{1}{R_{p}}=\dfrac{2+1}{6}}$

${:\implies \quad \sf \dfrac{1}{R_{p}}=\dfrac36}$

${:\implies \quad \sf \dfrac{1}{R_{p}}=\dfrac12}$

${:\implies \quad \boxed{\bf{R_{p}=2\Omega}}}$

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