Question

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 1

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

Answer 2

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+...}★ 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}+...}★

R

eq

1

=

R

1

1

+

R

2

1

+

R

3

1

+...

Ohms Law :

\bf \bigstar\ \; \blue{V=IR}★ V=IR

where ,

V denotes potential difference

I denotes current

R denotes resistance

Solution

When 3 and 6 Ω are connected in series ,

\begin{gathered}\rm R_{eq}=3+6\\\\\implies \bf R_{eq}=9\ \text{\O}mega\end{gathered}

R

eq

=3+6

⟹R

eq

=9 Ømega

When these are connected in parallel ,

\begin{gathered}\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\ \text{\O}mega\end{gathered}

R

eq

1

=

3

1

+

6

1

⟹

R

eq

1

=

6

3

⟹R

eq

=

3

6

⟹R

eq

=2 Ømega

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

__________________________

Eq. Resistance = 2 Ω

Potential Difference = 6 V

Apply Ohms Law ,

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

★ V=IR

eq

⟹6=I(2)

⟹I=

2

6

⟹I=3 A ★

So , Current = 3 A