Homework SourseA simple electrical circuit consists of a resistor connected
A simple electrical circuit consists of a resistor connected between the
terminals of a battery. The voltage V (in volts) is dropping at the rate of 0.01
volts per second as the battery wears out. At the same time the resistance R
(in ohms) is increasing at the rate of 2 ohms per second as the resistor heats
up. The power P (in watts) disippated by the circuit is given by P = V^2/R . How
much is the power changing when R = 5 and V = 4?
terminals of a battery. The voltage V (in volts) is dropping at the rate of 0.01
volts per second as the battery wears out. At the same time the resistance R
(in ohms) is increasing at the rate of 2 ohms per second as the resistor heats
up. The power P (in watts) disippated by the circuit is given by P = V^2/R . How
much is the power changing when R = 5 and V = 4?
Solution
p=v^2/r
dp/dt= (2v/r)dv/dt-(v/r)^2dr/dt
dp/dt=(8/5)(-.01)-(4/5)^2*2
=-1.44
