69. II The current through inductance is given by .
CALC a. Find an expression for the potential difference across the inductor.
b. The maximum voltage across the inductor is when and . What is ?
Part (a) The expression for potential difference across the inductor is
Part (b) The maximum voltage across the inductor is
The current in the inductor at any instant of time is
Here, is the angular frequency, is the time taken by the current in the inductor, and is the maximum current in the inductor.
Differentiate the equation with respect to time .
The potential difference across the inductance is
Therefore, the expression for potential difference across the inductor is
Convert the units for inductance from to .
Convert the units for frequency from to
The maximum cosine value varies from +1 to -1 . So the maximum potential difference across the inductor is,
Rewrite the equation for current
Therefore, the maximum voltage across the inductor is
A rectangular metal loop with resistance is placed next to one wire of the RC circuit shown in . The capacitor is charged to with the polarity shown, then the switch is closed at .
a. What is the direction of current in the loop for ?
b. What is the current in the loop at ? Assume that
only the circuit wire next to the loop is close enough to produce a significant magnetic field.
The switch in FIGURE P30.77 has been open for a long time. It is closed at .
a. After the switch has been closed for a long time, what is the current in the circuit? Call this current .
b. Find an expression for the current as a function of time. Write your expression in terms of .
c. Sketch a current-versus-time graph from until the current is no longer changing.
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