document.write( "Question 1099377: An inductor in an electric circuit VL=10-.5t for a 2 H inductor. Find the current in the circuit after 20 seconds if the initial current was zero.
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Algebra.Com's Answer #714225 by math_helper(2461) $\"\"$ $\"About$

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$\"+V%5BL%5D+=+L%2A%28di%2Fdt%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Which, after integration gives:
\n" ); document.write( " $\"++i+=+%281%2FL%29+%2A+%28i%5B0%5D+%2B+int%28+V%28t%29%2C+dt%2C+0%2C++T+%29%29++\"$ \r
\n" ); document.write( "\n" ); document.write( "We have
\n" ); document.write( " $\"+i%5B0%5D+=+0+\"$ amps
\n" ); document.write( " $\"+T+=+20+\"$ sec
\n" ); document.write( " $\"+V%28t%29+=+10-%281%2F2%29t+\"$ volts, assumed
\n" ); document.write( " $\"+L+=+2+\"$ Henries\r
\n" ); document.write( "\n" ); document.write( "So
\n" ); document.write( " $\"+i+=+%281%2F2%29+%2A%28+0+%2B+int%2810-%281%2F2%29t%2C+dt%2C+0%2C+20%29%29+\"$
\n" ); document.write( " $\"+i+=++%281%2F2%29+%2A%28++10t+-+%281%2F4%29t%5E2+%29+\"$ evaluated at t=20 and t=0
\n" ); document.write( " $\"++i+=+%281%2F2%29+%2A+%28%28200+-+%281%2F4%29%2820%5E2%29%29+-+%280+-+0%29%29+\"$ for $\"+t%3E=0+\"$
\n" ); document.write( " $\"+highlight%28+i+=+50%29+\"$ amps \r
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\n" ); document.write( "Below is a graph of i (y-axis) vs t (x-axis) (ignore the part to the left and below the origin, i[0] = 0).
\n" ); document.write( " It happens that i(t) is maximal at t=20sec, after that the current decays back down toward zero, and would go below zero after t=40sec IF the voltage source continued to obey 10-5t.
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