Electrical system are governed by Ohm's law, which states that V = IR, where V=voltate, I=current, and R=resistance. If the current in an electrical system is decreasing at a rate of 9 A/s while the voltage remains constant at 14 V, at what rate is the resistance increasing when the current is 40 A?

Question

Electrical system are governed by Ohm's law, which states that V = IR, where V=voltate, I=current, and R=resistance.  If the current in an electrical system is decreasing at a rate of 9 A/s while the voltage remains constant at 14 V, at what rate is the resistance increasing when the current is 40 A?

Reiny · Answer

so IR = 14 so when I = 40 R = 14/40 = 7/20 d(I)/dt(R) + d(R)/dt(I) = 0 -9(7/20) + d(R)/dt (40) = 0 d(R)/dt = 63/20 /40 = 63/800 resistance units/s