Question

According to Ohm's Law, in an electrical circuit the voltage V (in volts) is related to the current I (in amps) and the resistance R (in ohms) by V = TR. Sup pose that when the current is 5 amps and the resistance is 6 ohms, the current is increasing by 0.3 amps/minute. What will be the rate of change of the resistance at that moment if the voltage remains unchanged? Make sure your answer has units! .

Answer 1

The resistance is decreasing at a rate of 0.36 ohms/minute.

Explanation:

The mathematical form of the Ohm's law is given by :

V = IR ...(1)

Where V is voltage, I is current and R is resistance

Given,

I = 5 A

R = 6 ohms

dI/dt = 0.3 A/min

Differentiate equation (1) wrt t:

`(dV)/(dt)=I(dR)/(dt)+R(dI)/(dt)`

When V is constant, dV/dt = 0

`0=5* (dR)/(dt)+6* 0.3\ A/s\\\\1.8=-5* (dR)/(dt)\\\\(dR)/(dt)=-0.36\ \Omega/min`

So, the resistance is decreasing at a rate of 0.36 ohms/minute.