Advertisements
Advertisements
Question
Three resistances, of which two are equal when connected in series have an effective resistance of 30 ohms. When the three resistances are connected in parallel, the effective resistances is 3 ohms. Find the values of the individual resistances.
Advertisements
Solution
When connected in series, R = R1 + R1 + R2 (two are equal)
R = 2R1 + R2
∴ 2R1 + R2 = 30 ....(R = 30 Ω)
∴ 2R1 = 30 - R2
∴ R1 = `(30 - "R")/2` .....(i)
When connected in parallel,
`1/"R" = 1/"R"_1 + 1/"R"_1 + 1/"R"_2`
Or `1/"R" = 1/((30 - "R"_2)/2) + 1/((30 - "R"_2)/2) + 1/"R"_2` ....(From equation (i))
∴ `1/"R" = 2/(30 - "R"_2) + 2/(30 - "R"_2) + 1/"R"_2`
`1/3 = 4/(30 - "R"_2) + 1/"R"_2` ...(as R = 3Ω)
∴ `1/3 = (4"R"_2 + 30 - "R"_2)/("R"_2
(30 - "R"_2)) = (3"R"_2 + 30)/("R"_2(30 - "R"_2))`
∴ R2 `(30 - "R"_2)/3 = 9 "R"_2 + 90`
`30"R"_2 - "R"_2^2 = 9"R"_2 + 90`
`"R"_2^2 - 21 "R"_2 + 90 = 0`
∴ R2 - 6R2 - 15R2 + 90 = 0
∴ R2 = 6 or 15
∴ R1 = `(30 - 6)/2` or `(30 - 15)/2`
R1 = 12 Ω or 7.5 Ω
The three resistances can have values 12 Ω, 12 Ω and 6 Ω or 15 Ω, 7.5 Ω and 7.5 Ω.
APPEARS IN
RELATED QUESTIONS
Fill in the folloing blank with suitable words:
Current is measured in ............... using an ............... placed in ............... in a circuit.
How many electrons are flowing per second past a point in a circuit in which there is a current of 5 amp?
A p.d. of 6 V is applied to two resistors of 3 Ω and 6 Ω connected in parallel. Calculate:
(a) the combined resistance
(b) the current flowing in the main circuit
(c) the current flowing in the 3 Ω resistor.
Consider the circuit given below:
(a) In which circuit are the lamps dimmest?
(b) In which circuit or circuits are the lamps of equal brightness to the lamps in circuit (i)?
(c) Which circuit gives out the maximum light?
Christmas tree lamps are usually wired in series. What happens if one lamps breaks?
The diagram shows two ways of connecting three lamps P, Q and R to A.C. supply of 220 V.
My mother was operating washing machine on Sunday morning. Suddenly, she saw a spark coming out of the electric board and the electric current in the house failed. An electrician was called to look into the matter. What should he have noticed.
True or False – If False give the correct answer
The representation of the electric current is A
Assertion (A): Electric current will not flow between two charged bodies when connected if their charges are the same.
Reason (R): Current is the rate of flow of charge.
