Question
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.
✓
Answer
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 R1 and R2 If connected in series, then 9 = R1 + R2 R1 = 9 - R2 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 R2 6 ohms, then R1 = 9 - 6 = 3 ohms. If R2 = 3 ohms, then R1 = 9 - 3 = 6 ohms.Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
An electric heater is connected to the 230V mains supply. A current of 8A flows through the heater.
- How much charge flows around the circuit each second?
- How much energy is transferred to the heater each second?
Why is the colour of the clear sky blue?
A concave lens has a focal length of 20cm. At what distance from the lens a 5cm tall object be placed so that it forms an image at 15cm from the lens? Also calculate the size of the image formed.
Calculate the area of cross-section of a wire if its length is 1.0m, its resistance is $23 Ω$ and the resistivity of the material of the wire is $1.84\times10 Ω\ \text{m}.$
→A student uses a lens of focal length -50cm. What is the nature of the lens and its power?
Size of image of an object by a mirror having a focal length of 20cm is observed to be reduced to $\frac{1}{3}\text{rd}$ of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?
→A student made an electric circuit as shown below.
Is there any mistake in this circuit? If any then correct it.
Is there any mistake in this circuit? If any then correct it.
Define power of a lens. What is its unit? One student uses a lens of focal length 50cm and another of -50cm. What is the nature of the lens and its power used by each of them?
What is (a) the highest, (b) the lowest total resistance that can be secured by combinations of four coils of resistance 4Ω, 8Ω, 12Ω, 24Ω?
A piece of wire of resistance $20 Ω$ is drawn out so that its length is increased to twice its original length. Calculate the resistance of the wire in the new situation.
→