Two resistors of equal resistance are connected in series with each other and are connected to a battery that produces a potential difference of 8 V. If the current is 0.2 A what is the value of each resistance?
R1 = R2 = Vi/I = 0.5*8/0.2 = 20 Ohms.
To find the value of each resistance, we need to use Ohm's Law, which states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R).
In this case, we know the current (I) is 0.2 A and the potential difference (V) is 8 V. Since the two resistors are connected in series, the total resistance (R_total) is the sum of the individual resistances (R1 + R2).
Therefore, we can set up the equation as follows:
0.2 A = 8 V / (R1 + R2)
Since the two resistors are of equal resistance, we can assign the same value to both resistors. Let's call this value R.
0.2 A = 8 V / (2R)
To solve for R, we need to isolate it on one side of the equation. We can achieve this by cross-multiplying:
0.2A * 2R = 8 V
0.4R = 8 V
Finally, we can solve for R by dividing both sides of the equation by 0.4:
R = 8 V / 0.4
R = 20 Ω
Therefore, each resistor has a value of 20 Ω.