Question

Suppose that in a circuit having an inductor with inductance 0.0847 Henry and resistor with resistance 1.340 Ohms in series the current (in Amps) is changing as a function of timet (in seconds) according to l=-Ct. where C is a positive constant. If the potential difference across the inductor is measured to be 16.0 volis then what must be the value of C ?

Answer 1

The value of C needed to create a potential difference of 16.0 volts across an inductor with 0.0847 Henry of inductance is approximately 188.90 A/s, derived from the formula for induced voltage in an RL circuit.

Step-by-step explanation:

When a current I(t) through an inductor changes over time, the induced voltage (V) across an inductor can be calculated using the formula V = L * (dI/dt), where L is the inductance in henrys and dI/dt is the rate of change of current with respect to time. In this scenario, the current is changing according to the function I(t) = -Ct, which implies a constant rate of change of current because the derivative dI/dt is equal to -C. Given the measured potential difference of 16.0 volts across the inductor, we can find the value of C.

Using the formula for induced voltage, we have 16.0 V = 0.0847 H * -C. Solving for C gives us C = 16.0 V / 0.0847 H, which results in C being approximately 188.90 A/s. Therefore, the value needed for C to create a potential difference of 16.0 volts across an inductor with an inductance of 0.0847 Henry in an RL circuit is about 188.90 A/s.