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Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks?
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Derive an expression for the heat produced in a conductor of resistanc...
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Derive an expression for the heat produced in a conductor of resistanc...
Expression for the heat produced in a conductor:
When a current I flows through a conductor of resistance R for time t, the heat produced in the conductor can be calculated using the formula:
Q = I^2 * R * t
Where:
Q is the heat produced (in joules),
I is the current flowing through the conductor (in amperes),
R is the resistance of the conductor (in ohms), and
t is the time for which the current flows (in seconds).
Case 1: Two identical resistors connected in series
When two identical resistors of resistance R are connected in series with a battery of potential difference V for time T, the current flowing through each resistor can be calculated using Ohm's Law:
I = V / (2R)
Where:
I is the current flowing through each resistor (in amperes),
V is the potential difference across the series combination (in volts), and
2R is the total resistance of the series combination (since the resistors are identical).
The heat produced in each resistor can be calculated using the formula mentioned above:
Q1 = (V / (2R))^2 * R * T = V^2 * T / (4R)
Case 2: Two identical resistors connected in parallel
When the two identical resistors of resistance R are connected in parallel with the same battery for the same time T, the potential difference across each resistor remains the same as the battery's potential difference V.
The total resistance of the parallel combination can be calculated using the formula:
1/Rp = 1/R + 1/R = 2/R
Where:
1/Rp is the reciprocal of the total resistance of the parallel combination (in inverse ohms),
1/R is the reciprocal of the resistance of each resistor (since they are identical), and
2/R is the sum of the reciprocals of the resistances.
The current flowing through each resistor in parallel can be calculated using Ohm's Law:
I = V / Rp = V / (2R)
The heat produced in each resistor can be calculated using the formula mentioned above:
Q2 = (V / (2R))^2 * R * T = V^2 * T / (4R)
Comparison of the heat produced in two cases:
As we can see, the heat produced in both cases is the same, given by the expression V^2 * T / (4R). This implies that the arrangement of resistors (series or parallel) does not affect the total heat produced. The heat generated is solely determined by the potential difference across the resistors, the total resistance, and the time for which the current flows.
When a current I flows through a conductor of resistance R for time t, the heat produced in the conductor can be calculated using the formula:
Q = I^2 * R * t
Where:
Q is the heat produced (in joules),
I is the current flowing through the conductor (in amperes),
R is the resistance of the conductor (in ohms), and
t is the time for which the current flows (in seconds).
Case 1: Two identical resistors connected in series
When two identical resistors of resistance R are connected in series with a battery of potential difference V for time T, the current flowing through each resistor can be calculated using Ohm's Law:
I = V / (2R)
Where:
I is the current flowing through each resistor (in amperes),
V is the potential difference across the series combination (in volts), and
2R is the total resistance of the series combination (since the resistors are identical).
The heat produced in each resistor can be calculated using the formula mentioned above:
Q1 = (V / (2R))^2 * R * T = V^2 * T / (4R)
Case 2: Two identical resistors connected in parallel
When the two identical resistors of resistance R are connected in parallel with the same battery for the same time T, the potential difference across each resistor remains the same as the battery's potential difference V.
The total resistance of the parallel combination can be calculated using the formula:
1/Rp = 1/R + 1/R = 2/R
Where:
1/Rp is the reciprocal of the total resistance of the parallel combination (in inverse ohms),
1/R is the reciprocal of the resistance of each resistor (since they are identical), and
2/R is the sum of the reciprocals of the resistances.
The current flowing through each resistor in parallel can be calculated using Ohm's Law:
I = V / Rp = V / (2R)
The heat produced in each resistor can be calculated using the formula mentioned above:
Q2 = (V / (2R))^2 * R * T = V^2 * T / (4R)
Comparison of the heat produced in two cases:
As we can see, the heat produced in both cases is the same, given by the expression V^2 * T / (4R). This implies that the arrangement of resistors (series or parallel) does not affect the total heat produced. The heat generated is solely determined by the potential difference across the resistors, the total resistance, and the time for which the current flows.
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Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks?
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Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks? 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 Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks?.
Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks? 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 Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks?.
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Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks?, a detailed solution for Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks? has been provided alongside types of Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t two identical resistors of resistance R are connected in series with a battery of potential difference V for time T the resistors are then connected in parallel with the same battery for the same time we compared the heat produced in the two cases in detail its of 5 marks? theory, EduRev gives you an
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