Question

discuss growth and decay of current in a circuit containing an inductance and a resistance pdf

Answer 1

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e. Growth and Decay of Current In An LR Series Circuit. If a

battery is connected across a pure inductance, the current

builds up to its final value at a rate determined by the battery

voltage and the internal resistance of the battery. The current

buildup is gradual because of the counter emf generated by the

self­inductance of the coil. When the current starts to flow,

the magnetic lines of force move outward from the coil. These

lines cut the turns of wire on the inductor and build up a

counter emf that opposes the emf of the buttery. This

opposition causes a delay in the time it takes the current to

build up to a steady value. When the battery is disconnected,

the lines of force collapse. Again, these lines cut the turns

of the inductor and build up an emf that tends to prolong the

flow of current.

A voltage divider containing resistance and inductance may be

connected in a circuit by means of a special switch, as shown in

figure 20, view A, on the following page. Such a series

arrangement is called an inductance resistance (LR) circuit.

When switch S1 is closed (as shown), a voltage (Es) appears

across the voltage divider. A current attempts to flow, but the

inductor opposes the current by building up a back emf that, at

the initial instant, exactly equals the input voltage (ES). This

is the same as having two voltage sources of equal value and

opposite polarity. With this condition, no current will flow.

Because no current can flow, there is no voltage drop across

resistor R. View B, figure 20, shows that all of the voltage is

impressed across inductor L and no voltage appears across

resistance R at the instant switch S1 is closed.

As current starts to flow, a voltage (eR) appears across R, and

the voltage across the inductor is reduced by the same amount.

The fact that the voltage across the inductor (L) is reduced

means that the growth current (ig) is increased and consequently

eR is increased. View B, figure 20, shows that the voltage

across the inductor (eL ) finally becomes zero when the growth

current ig) stops increasing, while the voltage across the

resistor (eR) builds up to a value equal to the source voltage.