Engineering students at the University of Houston can take classes where they learn about the theory of electrical circuits. One topic they encounter in these courses is called “Ohm’s law,” and it describes the relationship between the voltage V across a resistor, the electrical current I passing through the resistor, and a quantity R known as the resistance. The law can be written as follows: V = I * R. Voltage is typically measured in volts, while current is measured in amperes (amps), and resistance is measured in ohms where 1 ohm equals 1 volt/amp. Lastly, in circuits with variable resistance, the quantities V, I, and R can depend on time. (a) Differentiate Ohm’s Law to find an equation relating the quantities V, I, R, dV/dt , dI/dt , and dR/dt . (b) Suppose that in an electrical circuit the current is increasing at a rate of 0.5 amps per second and the resistance is decreasing at a rate of 4 ohms per second. If at this same moment in time there are 3 volts of voltage and 2 ohms of resistance, what is the rate of change in voltage at this time? Is the voltage increasing or decreasing? (c) Suppose that in an electrical circuit the current is increasing at a rate of 0.5 amps per second and the voltage is decreasing at a rate of 2 volts per second. If at this same moment in time there are 3 volts of voltage and 2 ohms of resistance, what is the rate of change in resistance at this time? Is the resistance increasing or decreasing? Thank you so much for helping me!
Engineering students at the University of Houston can take classes where they learn about the theory of electrical circuits. One topic they encounter in these courses is called “Ohm’s law,” and it describes the relationship between the voltage V across a resistor, the
V = I * R.
Voltage is typically measured in volts, while current is measured in amperes (amps), and resistance is measured in ohms where 1 ohm equals 1 volt/amp. Lastly, in circuits with variable resistance, the quantities V, I, and R can depend on time.
(a) Differentiate Ohm’s Law to find an equation relating the quantities V, I, R, dV/dt , dI/dt , and dR/dt .
(b) Suppose that in an electrical circuit the current is increasing at a rate of 0.5 amps per second and the resistance is decreasing at a rate of 4 ohms per second. If at this same moment in time there are 3 volts of voltage and 2 ohms of resistance, what is the rate of change in voltage at this time? Is the voltage increasing or decreasing?
(c) Suppose that in an electrical circuit the current is increasing at a rate of 0.5 amps per second and the voltage is decreasing at a rate of 2 volts per second. If at this same moment in time there are 3 volts of voltage and 2 ohms of resistance, what is the rate of change in resistance at this time? Is the resistance increasing or decreasing?
Thank you so much for helping me!
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