Question

Two resistors with resistances 4Ω and 6 Ω are to be connected to a battery for minimum current flow and maximum current flow. The equivalent resistance in each case respectively are​

Answer 1

Given :

To resistors are connected in the circuit,

R₁ = 4 ohms

R₂ = 6 ohms

To find :

The equivalent resistance when it is connected to a battery for minimum current flow and maximum current flow.

Solution :

For minimum current these two resistors should be connected in series combination.

we know that,

» The combined resistance of any number of resistance connected in series is equal to the sum of the individual resistances. i.e.,

R = R₁ + R₂

By substituting the values in the formula,

$\dashrightarrow \sf R_{eq} = R_1 + R_2$

$\dashrightarrow \sf R_{eq} =4 + 6$

$\dashrightarrow \boxed{ \sf R_{eq} =10 \: ohms}$

For maximum current these two resistors should be connected in parallel combination.

»The reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. .i.e.,

1/R = 1/R₁ + 1/R₂

By substituting the values in the formula,

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{1}{R_{1}} + \dfrac{1}{ R_2}$

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{1}{4} + \dfrac{1}{6}$

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{3 + 2}{12}$

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{5}{12}$

$\dashrightarrow \sf R_{eq} = \dfrac{12}{5}$

$\dashrightarrow \boxed{\sf R_{eq} = 2.4 \: ohms}$

Answer 2

Answer:-

• Two resistors with resistances are connected in series and parallel.
• R1=4ohms
• R2=6ohms

In series connection:-

$\boxed{\sf R_{(Equivalent)}=R_1+R_2}$

$\\ \:\:\:\:\:\:\tt\longmapsto R_{(Equivalent)}=4+6$

$\\ \:\:\:\:\:\:\pmb{\tt\longmapsto R_{(Equivalent)}=10\Omega}$

In parallel connection:-

$\boxed{\sf \dfrac{1}{R_{(Equivalent)}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}$

$\\ \:\:\:\:\:\:\tt\longmapsto \dfrac{1}{R_{(Equivalent)}}=\dfrac{1}{4}+\dfrac{1}{6}$

$\\ \:\:\:\:\:\:\tt\longmapsto \dfrac{1}{R_{(Equivalent)}}=\dfrac{3+2}{12}$

$\\ \:\:\:\:\:\:\tt\longmapsto \dfrac{1}{R_{(Equivalent)}}=\dfrac{5}{12}$

$\\ \:\:\:\:\:\:\tt\longmapsto R_{(Equivalent)}=\dfrac{12}{5}$

$\\ \:\:\:\:\:\:\pmb{\tt\longmapsto R_{(Equivalent)}=2.4\Omega}$