a 25v heater has two elements, one of which is missing. if the resistance of the remaining element is measured to be 50 ohm,what must the resistance of a second element be when connected in parallel to maintain a current of 1 amp.
i = 25/Requivalent = 1 amp
so we need
Req = 25
In parallel
Req = R1R2/(R1+R2)
25 = 50 R2/(50+R2)
25 (50 + R2) = 50 R2
50 + R2 = 2 R2
R2 = 50
which we could have guessed :)
To solve this problem, we need to apply Ohm's Law, which states that the current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it and inversely proportional to the resistance (R) of the conductor. The formula for Ohm's Law is:
I = V / R
Given information:
- Voltage (V) = 25 volts
- Resistance of the remaining element (R1) = 50 ohms
- Current (I) = 1 ampere
To maintain the same current (1A) in a parallel circuit, we need to determine the resistance (R2) of the second element.
First, let's calculate the total resistance (Rt) when only one element (R1) is present in the circuit, using Ohm's Law:
Rt = V / I
Rt = 25 V / 1 A
Rt = 25 ohms
In a parallel circuit, the total resistance (Rt) can be calculated using the formula:
1 / Rt = 1 / R1 + 1 / R2
Substituting the known values:
1 / 25 = 1 / 50 + 1 / R2
Now solving for R2:
1 / R2 = 1 / 25 - 1 / 50
1 / R2 = (2 - 1) / 50
1 / R2 = 1 / 50
R2 = 50 ohms
Therefore, the resistance of the second element (R2) when connected in parallel to the remaining element with a resistance of 50 ohms is also 50 ohms.