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The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12?
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The maximum and minimum resistance obtained by connecting two resistan...
Analysis:
The maximum resistance obtained when two resistances are connected in parallel is given by the formula:
\[ \frac{1}{R_{\text{max}}} = \frac{1}{R_1} + \frac{1}{R_2} \]
The minimum resistance obtained when two resistances are connected in series is given by the formula:
\[ R_{\text{min}} = R_1 + R_2 \]
Solution:
Given:
- Maximum resistance = 6 ohms
- Minimum resistance = 4/3 ohms
Calculating Maximum Resistance:
\[ \frac{1}{6} = \frac{1}{R_1} + \frac{1}{R_2} \]
\[ \frac{1}{6} = \frac{1}{R_1} + \frac{1}{R_2} \]
\[ R_1R_2 = \frac{6R_1 + 6R_2}{6} \]
\[ R_1R_2 = R_1 + R_2 \]
\[ R_1 = 2R_2 \]
Substitute R1 = 2R2 in the equation for minimum resistance:
\[ 2R_2 + R_2 = 4/3 \]
\[ 3R_2 = 4/3 \]
\[ R_2 = 4/9 \]
Therefore, the values of R1 and R2 are 2 ohms and 4/9 ohms respectively.
Conclusion:
The correct option is (C) 2 ohms and 4/9 ohms.
The maximum resistance obtained when two resistances are connected in parallel is given by the formula:
\[ \frac{1}{R_{\text{max}}} = \frac{1}{R_1} + \frac{1}{R_2} \]
The minimum resistance obtained when two resistances are connected in series is given by the formula:
\[ R_{\text{min}} = R_1 + R_2 \]
Solution:
Given:
- Maximum resistance = 6 ohms
- Minimum resistance = 4/3 ohms
Calculating Maximum Resistance:
\[ \frac{1}{6} = \frac{1}{R_1} + \frac{1}{R_2} \]
\[ \frac{1}{6} = \frac{1}{R_1} + \frac{1}{R_2} \]
\[ R_1R_2 = \frac{6R_1 + 6R_2}{6} \]
\[ R_1R_2 = R_1 + R_2 \]
\[ R_1 = 2R_2 \]
Substitute R1 = 2R2 in the equation for minimum resistance:
\[ 2R_2 + R_2 = 4/3 \]
\[ 3R_2 = 4/3 \]
\[ R_2 = 4/9 \]
Therefore, the values of R1 and R2 are 2 ohms and 4/9 ohms respectively.
Conclusion:
The correct option is (C) 2 ohms and 4/9 ohms.
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The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12?
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The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12?.
The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum and minimum resistance obtained by connecting two resistances R. and R2 are 6 ohm and 4/3 ohm are respectively. The values of R1 R2 are 3 (B) * 4Omega 6 Ω (C) 6 Ω, 2 Ω (D) 8 2, 12?.
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