Two resistances when connected in parallel give resultant value of $2$ ohm; when connected in series the value becomes $9$ ohm. Calculate the value of each resistance.
Download our app for free and get started
Two resistance when connected in series, resultant value is $9$ ohms.
Two resistance when connected in parallel, resultant values is $2$ ohms.
Let the two resistance be $R_1$ and $R_2$
If connected in series, then
$9 = R_1+ R_2$
$R_1 = 9 - R_2$
If connected in parallel, then
$\frac{1}{2}=\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}$
From aboves equations we get that
$\frac{1}{2}=\frac{(\text{R}_1+\text{R}_2)}{\text{R}_1\text{R}_2}$
$\frac{1}{2}=\frac{9}{(9-\text{R}_2)\text{R}_2}$
$9\text{R}_2-\text{R}_2{^2}=18$
$\text{R}_2{^2}-9\text{R}_2+18=0$
$(\text{R}_2-6)(\text{R}_2-3)=0$
$\text{R}_2=6,3$
So if $R_2$ $6$ ohms, then $R_1 = 9 - 6 = 3$ ohms.
If $R_2 = 3$ ohms, then $R_1 = 9 - 3 = 6$ ohms.
Two resistance when connected in parallel, resultant values is $2$ ohms.
Let the two resistance be $R_1$ and $R_2$
If connected in series, then
$9 = R_1+ R_2$
$R_1 = 9 - R_2$
If connected in parallel, then
$\frac{1}{2}=\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}$
From aboves equations we get that
$\frac{1}{2}=\frac{(\text{R}_1+\text{R}_2)}{\text{R}_1\text{R}_2}$
$\frac{1}{2}=\frac{9}{(9-\text{R}_2)\text{R}_2}$
$9\text{R}_2-\text{R}_2{^2}=18$
$\text{R}_2{^2}-9\text{R}_2+18=0$
$(\text{R}_2-6)(\text{R}_2-3)=0$
$\text{R}_2=6,3$
So if $R_2$ $6$ ohms, then $R_1 = 9 - 6 = 3$ ohms.
If $R_2 = 3$ ohms, then $R_1 = 9 - 3 = 6$ ohms.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Calculate the resistance of an aluminium cable of length $10\ km$ and diameter $2.0\ mm$ if the resistivity of aluminium is $2.7\times10 Ω\ \text{m}.$View Solution
- 2View SolutionWhat is Ohm’s law? Explain how it is used to define the unit of resistance.
- 3View SolutionConsider the circuit given below where A, B and C are three identical light bulbs of constant resistance.
- List the bulbs in order of increasing brightness.
- If C burns out, what will be the brightness of A now compared with before?
- If B burns out instead, what will be the brightness of A and C compared with before?
- 4View SolutionDraw circuit symbols for:
- Fixed resistance.
- Variable resistance.
- A cell.
- A battery of three cells.
- An open switch.
- A closed switch.
- 5If the charge on an electron is $1.6 \times 10$ coulombs, how many electrons should pass through a conductor in $1$ second to constitute $1$ ampere current?View Solution
- 6View SolutionIf a potential difference of 10V causes a current of 2A to flow for 1 minute, how much energy is transferred?
- 7For the circuit shown in the diagram below:View Solution
What is the value of :
Current through $6 Ω$ resistor?
Potential difference across $12 Ω$ resistor? - 8Calculate the power used in the $2Ω$ resistor in each of the following circuits:View Solution
- A $6V$ battery in series with $1Ω$ and $2Ω$ resistors.
- A $4V$ battery in parallel with $12Ω$ and $2Ω$ resistors.
- 9View SolutionDistinguish between good conductors, resistors and insulators. Name two good conductors, two resistors and two insulators.
- 10View SolutionGive three reasons why different electrical appliances in a domestic circuit are connected in parallel.