Voltage Across Inductor After Long Time

9 2009 physics 208 lecture 20 2 dv l v b v a l di dt rl circuit. With only one resistor in our example circuit having a value of 1 w this is rather easy.

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From last time inductors in circuits inductors flux inductance x current fli v batt r l i v b v a voltage drop across inductor constant current no voltage difference current changing in time voltage difference across inductor tue.

Voltage across inductor after long time. Energy stored in inductor 0510h09a2 405 j when inductor discharges through the resistor all this stored energy is dissipated as heat 405 j. Again after 5 time constants the circuit is considered to have reached equilibrium or constant state. Current is constant there is 0 v across the inductor and 10 v.

No current is flowing there is 10 v across the inductor and 0 v across the resistor. Then the voltage across the inductor v l will have an initial value equal to the battery voltage at time t 0 or when the switch is first closed and then decays exponentially to zero as represented in the above curves. Using ohms law the current in resistor 1 is ivr i108a a long time after the switch is closed the inductor now acts like a wire and r1 r2 are in paralell therefore i108 a and i2048 a v2 12v and vl 0v.

When switch has been in position a for long time current through inductor 9v10w 09a. For all practical purposes though we can say that the inductor voltage will eventually reach 0 volts and that the current will eventually equal the maximum of 15 amps. You could also say that the inductor current lags voltage by 90 degrees.

Just as with the rc circuit the inductor voltages approach to 0 volts and the currents approach to 15 amps over time is asymptotic. Subtracted from our battery voltage of 15 volts this leaves 0453 volts across the inductor at time35 seconds. So just after t0 no current passes through the inductor so the vl12v and v20v.

The current induces a voltage over the inductor which leads the current by 90 degrees. 9 v 10 w 10 h. Rate of increase of current didt vl.

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