Question

Judge the equivalent resistance when the following are connected in parallel.
(a) 1 Omega and 10^6 Omega
(b) 1 Omega and 10^8 Omega and 10^6 Omega.


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Answer 1

Answer:

Judge the equivalent resistance when the following are connected in parallel.

(a) 1 Omega and 10^6 Omega

(b) 1 Omega and 10^8 Omega and 10^6 Omega.

Answer:

Explanation:

First, let us know the setup of the question.

For series :- \sf{R_{eq} = R_1 + R_2}Req=R1+R2

Where R1, R-eq and R2 are the resistances in the wires respectively.

Now, for Parallel combination :-

\sf{\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}}Req1=R11+R21

Now, in this question, we need to deal with Parallel arrangement first, to evade complexity.

\sf{\dfrac{1}{R_{eq}} = \dfrac{1}{6} + \dfrac{1}{3}}Req1=61+31

\sf{\dfrac{1}{R_{eq}} = \dfrac{2+1}{6}}Req1=62+1

\sf{\dfrac{1}{R_{eq}} = \dfrac{3}{6}}Req1=63

\sf{\dfrac{1}{R_{eq}} = \dfrac{1}{2}}Req1=21

\sf{R_{eq} = 2 \text{\O}mega}Req=2Ømega

Now, we can apply the formula for series combination, which will be

\sf{R_{eq} = R_1 + R_2}Req=R1+R2

\sf{R_{eq} = 2 + 1}Req=2+1 (One from the question, other we determined previously)

\boxed{\sf{R_{eq} = 3 \text{\O}mega}}Req=3Ømega is the answer.