Five identical resistors, each of resistance R, are connected in series to a battery, and a total current of 9.74 A flows in the circuit.
i. Now, another resistor of resistance R is added to the circuit, in series with the rest of the resistors. Find the new total current in the circuit. I =
I = E/5R = 9.74 Amps
E = 5R * 9.74 = 48.7R
I = E/6R = 48.7R/6R = 8.12 Amps.
To find the new total current in the circuit after adding another resistor, we can use Ohm's Law and the concept of resistance in series.
In a series circuit, the total resistance (RT) is equal to the sum of the individual resistances. Since all the resistors are identical, each resistor has a resistance of R. So when we add another resistor, the total resistance becomes (5R + R) = 6R.
Ohm's Law states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R): I = V/R.
Since the voltage is constant in this case, we can rewrite Ohm's Law as I1/I2 = R2/R1, where I1 is the initial total current (9.74 A), I2 is the new total current (which we want to find), R1 is the initial total resistance (5R), and R2 is the new total resistance (6R).
Simplifying the equation, we have I2 = (I1 * R2) / R1.
Plugging in the values, we get:
I2 = (9.74 A * 6R) / (5R)
Simplifying further, we have:
I2 = 11.688 A
Therefore, the new total current in the circuit is approximately 11.688 A.