You have a 50V battery in a circuit with a single resistor R. If the resistor dissipates 200 J of energy in 5 seconds, what is its resistance?
The power is P = E/time = 40 watts
Use P = V^2/R to solve for R.
To determine the resistance of the resistor, we can use Ohm's Law, which states that the current flowing through a conductor (in this case the resistor) is equal to the voltage across the conductor divided by its resistance.
Ohm's Law equation: V = I * R
Where:
V is the voltage across the conductor (in volts),
I is the current flowing through the conductor (in amperes),
R is the resistance of the conductor (in ohms).
In this case, we know the voltage (V = 50V) and the time (t = 5 seconds) for which the resistor dissipates energy (power). We can calculate the power using the formula:
Power (P) = Energy (E) / Time (t)
Given that the resistor dissipates 200 J of energy in 5 seconds, we can calculate the power as:
P = 200 J / 5 s = 40 Watts (W)
Now, let's find the current flowing through the resistor by rearranging the power formula:
Power (P) = V * I
Therefore,
I = P / V
Substituting the known values:
I = 40 W / 50 V = 0.8 A
Now, we can use Ohm's Law to find the resistance:
R = V / I
Substituting the known values:
R = 50 V / 0.8 A = 62.5 ohms
Therefore, the resistance of the resistor is 62.5 ohms.