A coil with an inductance of 3 H and a wire resistance of 15 ohms takes how long to reach its full current value?

To understand how long it takes for a coil with an inductance of 3 H and a wire resistance of 15 ohms to reach its full current value, we can refer to the time constant of an RL circuit. The time constant (( \tau )) for an RL circuit is given by the formula:

[

\tau = \frac{L}{R}

]

where ( L ) is the inductance in henries (H) and ( R ) is the resistance in ohms (Ω). In this case:

[

\tau = \frac{3 , \text{H}}{15 , \text{Ω}} = 0.2 , \text{seconds}

]

The time constant indicates how quickly the current in the circuit reaches a significant fraction (about 63.2%) of its maximum value. Full current value is typically considered to be reached after approximately 5 time constants, as it takes this long for the current to virtually stabilize at its maximum level. Therefore, we multiply the time constant by 5:

[

\text{Total time} = 5 \cdot 0.2 , \text{s} = 1.0 \