1.

Two resistors of resistance 3ohm and 6 ohm are connected to a battery of 6 V , so as to have minimum resistance. Show how will you connect them(diagram) and also find the current in this case.

Answer»

Given

Two resistors of resistance 3 OHM and 6 Ohm are connected to a battery of 6 V

To Find

How to connect them for getting MINIMUM resistance

Knowledge Required

When resistors are connected in series ,

\bf \bigstar\ \; \pink{R_{eq}=R_1+R_2+R_3+...}

When resistors are connected in parallel ,

\bf \bigstar\ \; \green{\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+...}

Ohms Law :

\bf \bigstar\ \; \blue{V=IR}

where ,

V denotes potential DIFFERENCE

I denotes current

R denotes resistance

Solution

When 3 and 6 Ω are connected in series ,

\rm R_{eq}=3+6\\\\\implies \bf R_{eq}=9\ \Omega

When these are connected in parallel ,

\rm \dfrac{1}{R_{eq}}=\dfrac{1}{3}+\dfrac{1}{6}\\\\\implies \rm \dfrac{1}{R_{eq}}=\dfrac{3}{6}\\\\\implies \rm R_{eq}=\dfrac{6}{3}\\\\\implies \bf R_{eq}=2\ \Omega

So , We will get minimum resistance , when connected in parallel .

__________________________

  • Eq. Resistance = 2 Ω
  • Potential Difference = 6 V

Apply Ohms Law ,

\bf \red{\bigstar\ \; V=IR_{eq}}\\\\\rm \implies 6=I(2)\\\\\implies \rm I=\dfrac{6}{2}\\\\\implies \bf \orange{I=3\ A\ \; \bigstar}

So , Current = 3 A


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