Three resistors 10 ohm, 10 ohm, and 5 ohm connected in parallel. The effictive resistance will be *
2 ohm
2.5 ohm
5 ohm
10 ohm
Answers
Three resistors 10 ohm, 10 ohm and 5 ohm are connected in parallel.
Let's denote 10 ohm by R1 another 10 ohm resistor by R2 and 5 ohm resistor by R3. All of them are connected in parallel as shown:
----------------| R1 |----------------
----------------| R2 |----------------
----------------| R3 |----------------
We have to find the effective resistance of these three resistors.
Req = 1/R1 + 1/R2 + 1/R3
Req = (R1 + R2 + R3)/(R1R2R3)
Req = R1R2R3/(R1 + R2 + R3) ......(1st equation)
For series combination:
Rs = R1 + R2 + R3
But in question we are talking about parallel combination. So,
For parallel combination:
1/Rp = 1/R1 + 1/R2 + 1/R3
1/Rp = (R1 + R2 + R3)/(R1R2R3)
Rp = R1R2R3/(R1 + R2 + R3) ......(2nd equation)
Substitute the known values,
1/Rp = 1/10 + 1/10 + 1/5
Take L.C.M. as 10
1/Rp = (1 + 1 + 2)/10
1/Rp = 4/10
Rp = 10/4
Rp = 2.5 ohm
From (1st equation) and (2nd equation) we can say that,
Req = Rp
Req = 2.5 ohm
Therefore, the effective resistance is 2.5 ohm.
Option (b) 2.5 ohm
Answer:
- The Effective Resistance will be 2.5 Ω
Given:
- Given resistance:- 10 Ω, 10 Ω and 5 Ω.
Explanation:
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As given there are Three resistors which are connected in Parallel.
From the Formula, we know,'
⇒ 1/R = 1/R₁ + 1/R₂ + 1/R₃
Here,
- R Denotes Effective resistance.
- R₁ is given resistance.
- R₂ is given resistance.
- R₃ is given resistance.
Substituting the values,
⇒ 1/R = 1/10 + 1/10 + 1/5
Taking L.C.M
⇒ 1/R = ( 1 + 1 + 2 )/10
⇒ 1/R = 4/10
Reciprocating it,
⇒ R = 10/4
⇒ R = 2.5
⇒ R = 2.5 Ω
∴ The Effective Resistance will be 2.5 Ω.
Hence 2nd Option is correct !
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Some Formulas:
- For Series connection: R = R₁ + R₂ ..... + Rₓ
- V = I R
- P = V² / R
- P = V I
- H = I² R t
- H = ( V² / R ) t
Note:
- Symbols have their usual meanings.
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