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(A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?
(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same?
(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same?
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(A) A potential source is connected in parallel V by two wires of the ...
Part A: Equivalent Resistivity in Parallel Configuration
In a parallel configuration, the total or equivalent resistance can be calculated using the formula for resistors in parallel:
- The formula for equivalent resistance (R_eq) in parallel is given by:
1/R_eq = 1/R1 + 1/R2
Where R1 and R2 are the resistances of the wires.
- Given resistivities (ρ):
- Wire 1: ρ1 = 1
- Wire 2: ρ2 = 2
- Since the wires have the same length (L) and area (A), their resistances can be expressed as:
R1 = ρ1 * (L/A) = 1 * (L/A)
R2 = ρ2 * (L/A) = 2 * (L/A)
- Substituting these into the parallel resistance formula:
1/R_eq = 1/(L/A) + 1/(2L/A)
Which simplifies to:
1/R_eq = (2 + 1) / (2L/A) = 3 / (2L/A)
- Thus, R_eq = (2L)/(3A).
- The equivalent resistivity (ρ_eq) can be found by rearranging the formula:
ρ_eq = R_eq * (A/L) = (2/3) * 1 = 0.67.
Part B: Equivalent Resistivity in Series Configuration
In a series configuration, the total resistance is simply the sum of the individual resistances:
- The formula for equivalent resistance (R_eq) in series is:
R_eq = R1 + R2
- With the same resistivities:
- Wire 1: ρ1 = 1
- Wire 2: ρ2 = 2
- The resistances are:
R1 = 1 * (L/A)
R2 = 2 * (L/A)
- Therefore, the total resistance becomes:
R_eq = (1 * L/A) + (2 * L/A) = (3 * L/A).
- To find the equivalent resistivity (ρ_eq), we use the relationship:
ρ_eq = R_eq * (A/L) = (3 * L/A) * (A/L) = 3.
In summary, the equivalent resistivities are:
- Part A (Parallel): 0.67
- Part B (Series): 3.
In a parallel configuration, the total or equivalent resistance can be calculated using the formula for resistors in parallel:
- The formula for equivalent resistance (R_eq) in parallel is given by:
1/R_eq = 1/R1 + 1/R2
Where R1 and R2 are the resistances of the wires.
- Given resistivities (ρ):
- Wire 1: ρ1 = 1
- Wire 2: ρ2 = 2
- Since the wires have the same length (L) and area (A), their resistances can be expressed as:
R1 = ρ1 * (L/A) = 1 * (L/A)
R2 = ρ2 * (L/A) = 2 * (L/A)
- Substituting these into the parallel resistance formula:
1/R_eq = 1/(L/A) + 1/(2L/A)
Which simplifies to:
1/R_eq = (2 + 1) / (2L/A) = 3 / (2L/A)
- Thus, R_eq = (2L)/(3A).
- The equivalent resistivity (ρ_eq) can be found by rearranging the formula:
ρ_eq = R_eq * (A/L) = (2/3) * 1 = 0.67.
Part B: Equivalent Resistivity in Series Configuration
In a series configuration, the total resistance is simply the sum of the individual resistances:
- The formula for equivalent resistance (R_eq) in series is:
R_eq = R1 + R2
- With the same resistivities:
- Wire 1: ρ1 = 1
- Wire 2: ρ2 = 2
- The resistances are:
R1 = 1 * (L/A)
R2 = 2 * (L/A)
- Therefore, the total resistance becomes:
R_eq = (1 * L/A) + (2 * L/A) = (3 * L/A).
- To find the equivalent resistivity (ρ_eq), we use the relationship:
ρ_eq = R_eq * (A/L) = (3 * L/A) * (A/L) = 3.
In summary, the equivalent resistivities are:
- Part A (Parallel): 0.67
- Part B (Series): 3.
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(A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same?
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(A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about (A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same?.
(A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about (A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (A) A potential source is connected in parallel V by two wires of the same length and area made of materials with resistivities of 1 and 2, respectively. What would the equivalent resistivity be if the length and area were the same?(B) A source of potential V is connected in series with two wires that are of the same length and area but made of different resistivity materials (1 and 2). What would the equivalent resistivity be if the area were the same?.
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