In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 2A (amperes), the resistance is 115ohms. What is the resistance when the current is 5A ?
varies inversely means there is a constant k such that
ir = k
we are told that i=2 when r=115:
2*115 = 230 = k
so, when i=5,
5r = 230
r = 46 ohms
To find the resistance when the current is 5A, considering an inverse relationship, we can use the formula:
Current1 * Resistance1 = Current2 * Resistance2
Given that when the current is 2A, the resistance is 115 ohms, we can plug in the values into the formula:
2A * 115ohms = 5A * Resistance2
Simplifying the equation, we have:
230 = 5A * Resistance2
Next, we can solve for Resistance2 by dividing both sides of the equation by 5A:
Resistance2 = 230/5A
Therefore, when the current is 5A, the resistance is 230/5A ohms, or 46 ohms.