How does the current change if the resistance is halved?
I = E/R
now replace R with R/2, and the new current is
E/(R/2) = 2 E/R
so the current doubles
To understand how the current changes when the resistance is halved, we can use Ohm's Law. Ohm's Law states that the current (I) flowing through a conductor is directly proportional to the voltage (V) across the conductor, and inversely proportional to the resistance (R) of the conductor. Mathematically, it can be represented as:
I = V / R
Now, if we assume that the voltage across the conductor remains constant, we can observe the effect of resistance on the current. When the resistance is halved, the denominator of the equation becomes half its original value, which means the overall fraction becomes larger.
For example, let's say the initial resistance is R, and the initial current is I. According to Ohm's Law, I = V / R.
When the resistance is halved, it becomes R/2. Hence, the new current can be calculated as I_new = V / (R/2), which simplifies to I_new = 2V / R.
Comparing the initial current (I) to the new current (I_new), we can see that the new current is twice as large as the initial current. Therefore, when the resistance is halved, the current doubles, assuming the voltage remains constant.