In the circuit shown in the figure the heat produced in 5ohm resistor ...
Given information:- Resistance of the first resistor (R1) = 5 ohms
- Heat produced in R1 due to the current flowing through it = 10 calories per second
To find:- Heat generated in the second resistor (R2)
Explanation:
The amount of heat produced in a resistor is given by the formula:
Heat (H) = I^2 * R * tWhere:
- H is the heat produced in calories
- I is the current flowing through the resistor in amperes
- R is the resistance of the resistor in ohms
- t is the time in seconds
In this case, the heat produced in R1 is given as 10 calories per second. We can rearrange the formula to solve for the current flowing through R1:
I = sqrt(H / (R1 * t))Let's assume the time is 1 second for simplicity. Substituting the given values:
I = sqrt(10 / (5 * 1)) = sqrt(2) ≈ 1.414 ANow, we can use the current value to calculate the heat generated in R2. The resistance of R2 is given as 4 ohms:
Heat (H2) = I^2 * R2 * tSubstituting the calculated current value and assuming the time is 1 second:
H2 = (1.414)^2 * 4 * 1 = 2 * 4 = 8 calories per secondTherefore, the heat generated in the 4-ohm resistor (R2) is 8 calories per second.
Summary:The heat generated in the 4-ohm resistor (R2) is 8 calories per second when the heat produced in the 5-ohm resistor (R1) is 10 calories per second.