A heating instrument has 12 resistors and they are placed vertically and they have uniform reducing power.The power of the first, second,third and fourth resistors are 300ohms,260ohms,220ohms and 180ohms respectively.Find the power of the resistor?
How does one connect vertically resistors? What does "uniform reducing power" mean?
To find the power of the resistor, we need to calculate the resistance of each individual resistor and then find the power using the formula P = (V^2)/R, where P is power, V is voltage, and R is resistance.
Given that the resistors have uniform reducing power, we can assume that each resistor has a constant reduction in resistance. The reduction seems to be 40ohms for each resistor.
We have the following resistors:
First resistor: 300ohms
Second resistor: 260ohms
Third resistor: 220ohms
Fourth resistor: 180ohms
To find the resistance of each individual resistor, we can subtract the reduction from the initial resistance:
First resistor resistance = 300ohms - (0 * 40) = 300ohms
Second resistor resistance = 260ohms - (1 * 40) = 220ohms
Third resistor resistance = 220ohms - (2 * 40) = 140ohms
Fourth resistor resistance = 180ohms - (3 * 40) = 60ohms
Now, let's assume a constant voltage of 10V for all the resistors (this value is chosen for simplicity). We can calculate the power of each resistor using the given formula:
First resistor power = (V^2) / R = (10^2) / 300 = 100 / 300 = 1/3 W
Second resistor power = (10^2) / 220 = 100 / 220 = 5/11 W
Third resistor power = (10^2) / 140 = 100 / 140 = 5/7 W
Fourth resistor power = (10^2) / 60 = 100 / 60 = 5/3 W
Therefore, the power of the resistor is:
1/3 W, 5/11 W, 5/7 W, and 5/3 W for the first, second, third, and fourth resistors, respectively.