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(a) In Figure 30-28a, assume that the switch S has been in position A for suffic

ID: 1701796 • Letter: #

Question

(a) In Figure 30-28a, assume that the switch S has been in position A for sufficient time so that a steady current I0= V0/R flows through the resistor R. At time t=0. the switch is quickly switched to position B and the current through R decays according to I= I0*e-t/.

Show that the maximum emf induced in the inductor during this time period equals the battery voltage V0.

(b) In Figure 30-28b, assume that the switch has been in position A for sufficient time so that a steady current I0= V0/R flows through the resistor R. At time t=0. the switch is quickly switched to position B and the current decays through resistor R' (which is much greater than R) according to I=I0*e-t/'.

Show that the maximum emf induced in the inductor during this time period is (R'/R)V0. If R'= 55R and V0= 120V, determine emf max.

(a) In Figure 30-28a, assume that the switch S has been in position A for sufficient time so that a steady current I0= V0/R flows through the resistor R. At time t=0. the switch is quickly switched to position B and the current through R decays according to I= I0*e-t/?. Show that the maximum emf induced in the inductor during this time period equals the battery voltage V0. (b) In Figure 30-28b, assume that the switch has been in position A for sufficient time so that a steady current I0= V0/R flows through the resistor R. At time t=0. the switch is quickly switched to position B and the current decays through resistor R' (which is much greater than R) according to I=I0*e-t/?'. Show that the maximum emf epsilon max induced in the inductor during this time period is (R'/R)V0. If R'= 55R and V0= 120V, determine epsilonmax.

Explanation / Answer

the emf in the inductor as a function time . since the exponential term decrease in the time the maxiumum emf occurs when t= o

    = -L di/dt

   = - L d/dt ( I0 e-tR/L )

   = LI0 R/L * e-t/

   = v0e-t/

= max = v0

b) the current is the same just before and just after the   switch moves from A to B. we use ohms law for steady state current to determine I0 before switch is thrown. after the switch is thrown the same current flows through the inductor and there fore that current will flow through the resistor R1

usa kirchoffs loop rule we caliculate the emf in the inductor , this will be maxiumum at t= 0

I0 = V0/R

- IR1 = 0

= R1 ( V0/R)e-t/

( max) = R1/R * v0

   = 55R/R* 120v = 6.6kV