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 $R_1$ and $R_2$ If connected in series, then $9=R_1+R_2 R_1=9-R_2$ If connected in parallel, then $\frac{1}{2}=\frac{1}{R_1}+\frac{1}{R_2}$
From aboves equations we get that $\frac{1}{2}=\frac{\left( R _1+ R _2\right)}{ R _1 R _2}$
$\frac{1}{2}=\frac{9}{\left(9-R_2\right) R_2}$
$9 R_2-R_2^2=18$
$R_2^2-9 R_2+18=0$
$\left(R_2-6\right)\left(R_2-3\right)=0$
$R_2=6,3$
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.
From aboves equations we get that $\frac{1}{2}=\frac{\left( R _1+ R _2\right)}{ R _1 R _2}$
$\frac{1}{2}=\frac{9}{\left(9-R_2\right) R_2}$
$9 R_2-R_2^2=18$
$R_2^2-9 R_2+18=0$
$\left(R_2-6\right)\left(R_2-3\right)=0$
$R_2=6,3$
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.
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
Draw a ray diagram showing the path of rays of light when it enters with oblique incidence:
- From air into water;
- From water into air.
If in figure,$R _1=10 \Omega, R _2=40 \Omega, R _3=30 \Omega, R _4=20 \Omega, R _5=60 \Omega$, and a 12 V battery is connected to the arrangement. Calculate
a. the total resistance in the circuit, and
b. the total current flowing in the circuit.
→a. the total resistance in the circuit, and
b. the total current flowing in the circuit.
Give reasons:
Use of a mild base like baking soda provides relief on the area stung by honeybee.
Use of a mild base like baking soda provides relief on the area stung by honeybee.
Draw the ray diagram and also state the position, the relative size and the nature of image formed by a concave mirror when the object is placed at the centre of curvature of the mirror.
Atoms of eight elements A, B, C, D, E, F, G and H have the same number of electronic shells but different number of electrons in their outermost shell. It was found that elements A and G combine to form an ionic compound. This compound is added in’ a small amount to almost all vegetable dishes during cooking. Oxides of elements A and B are basic in nature while those of E and F are acidic. The oxide of D is almost neutral. Based on the above information answer the following questions:
- To which group or period of the periodic table do the listed elements belong?
- What would be the nature of compound formed by a combination of elements B and F?
- Which two of these elements could definitely be metals?
- Which one of the eight elements is most likely to be found in gaseous state at room temperature?
- If the number of electrons in the outermost shell of elements C and G be 3 and 7 respectively, write the formula of the compound formed by the combination of C and G.
What are the factors which govern the force experienced by a current carrying conductor placed in a uniform magnetic field depends?
Draw a ray diagram showing the dispersion through a prism when a narrow beam of white light is incident on one of its refracting surfaces. Also indicate the order of the colours of the spectrum obtained.
How is copper obtained from its ore $(Cu_2S)$? Write only the chemical equations. How is copper thus obtained refined? Name and explain the process alongwith a labelled diagram.
→Which uses more energy: a 250W TV set in 1 hour or a 1200W to aster in 10 minutes?
The atomic number of an element is 16. Predict:
- The number of valence electrons in its atom.
- Its valency.
- Its group number.
- Whether it is a metal ora non-metal.
- The nature of oxide formed by it.
- The formula of its chloride.