Question

find the total resistance of 9 ohm and 2 by 5 ohm when they are connected in series​

Answer 1

★ Provided Question ★

Find the total resistance of 9 ohm and 2 by 5 ohm when they are connected in series.

★ Required Answer ★

${\underline {\underline {\large {\bf{\red { Given :} }}}}}$

• Two resistors 9Ω and 2/5Ω are connected in series.

${\underline {\underline {\large {\bf {\red {To \: find:} }}}}}$

• Total resistance (R)

${\underline {\underline {\large {\bf {\red {Calculation:} }}}}}$

First of all, let's assume the 9Ω resistor as $\rm \blue { R_1 }$ and $\rm { \dfrac{2}{5} }$ Ω resistor as $\rm \blue { R_2 }$.

So, we have:–

• $\rm { R_1 }$ = $\rm { 9Ω }$

• $\rm { R_2 }$ = $\rm { \dfrac{2}{5} Ω}$

Now as they are in series combination, so we'll apply the formula or resultant resistance in series combination. That is:–

• ${\boxed {\huge {\bf {\pink { R_s = R_1 + R_2 + R_3..........}}}}}$

Now, substitute the values of $\rm { R_1 }$ and $\rm { R_2 }$ :

$\rm { :\implies R_s = R_1 + R_2 }$

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$\rm { :\implies R_s = 9Ω + \dfrac{2}{5} Ω }$

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$\rm { :\implies R_s = \dfrac{45+ 2}{5} Ω }$

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$\rm { :\implies R_s = \dfrac{47 }{5} Ω }$

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$\rm \purple { :\implies R_s = 9.4Ω }$ $\rm \purple { ★}$

Thus, the total resistance if two resistors 9Ω and 2/5Ω are connected in series is $\rm \purple { 9.4Ω }$.

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More Information:

• The property of a conductor due to which it opposes the flow of current through it is called resistance.

• The resistance of a conductor depends on the length, thickness,temperature and nature of the material of the conductor.

• The SI unit of resistance is ohm (Ω).

• Resistance can be in two combination:

✤ Series combination:

The sum of individual resistances is equal to the total resistance in the series combination.

Formula: ${\boxed {\large {\bf {\purple { R_s = R_1 + R_2 + R_3..........}}}}}$

✤ Parallel combination:

The sum of the reciprocals of all the individual resistances is equal to the reciprocal of the total resistance in the parallel combination.

Formula: ${\boxed {\large {\bf {\purple { \dfrac{1}{R_p} = \dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3} ..........}}}}}$

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Answer 2

Question :-

Find the total resistance of 9 ohm and 2 by 5 ohm when they are connected in series

Answer :-

Total Resistance = 9.4 Ω

Given :-

Two resistors = 9 Ω and ⅖ Ω

Have to Find :-

What's the total Resistance in the circuit ?

Calculations :-

As we know that the circuits are connected in series so ,

RT = R1 + R2 + R3.

9 Ω  , ⅖ Ω ( In Figure ) ,

↠$\frac{45 \: + \: 2}{ \: 5 \: }$

↠ $\frac{47}{5}$ Ω

↬ 9.4 Ω

Additional Information :-

✮ What is Resistance ?

Resistance refer to the property of materials that allow the flow of electric current. Resistance certainly opposes the flow of current. Furthermore, the unit of resistance is ohms which is represented by the Greek uppercase letter omega Ω.

✮ Formula for Resistance ?

Resistance = voltage drop across a resistor/ current flowing through a resistor

➤ R = V/I

➤ R = resistance (Ohms, Ω)

➤ V = voltage difference which is between the two ends of a resistor (Volts, V)

➤ I = the current which flows through a resistor (Amperes, A)

✮ Formula to find resistance in a series circuit ?

Series circuits

The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: equivalent resistance of resistors in series :

• R = R1 + R2 + R3 + .

A series circuit is shown in the diagram above. The current flows through each resistor in turn.

✮ Formula to find resistance in a parallel circuit ?

You can find total resistance in a Parallel circuit with the following formula:

• 1/Rt = 1/R1 + 1/R2 + 1/R3 +.

Note :-

If one of the parallel paths is broken, current will continue to flow in all the other paths.

The total resistance of a parallel circuit is NOT equal to the sum of the resistors (like in a series circuit).

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