A40.0-μfcapacitor is connected across a 60.0 hz generator. an inductor is then connected in parallel with the capacitor. what is the value of the inductance if the rms currents in the inductor and capacitor are equal?

The value of the inductance is 175.9 mH.

Explanation:

Given that,

Capacitor

Frequency = 60.0 Hz

The inductor and capacitor is connected in parallel, the voltage across each of these elements is the same.

We have,

Using ohm's law

Put the value into the formula

Hence, The value of the inductance is 175.9 mH.

The collision will occur 7.12 s from the moment Sue sees the van.

The collision will occur 196.9 m inside the tunnel.

Explanation:

The equation for the position of an object moving in a straight line is the following:

x = x0 + v0 · t + 1/2 · a · t²

Where

x = position at time t

x0 = initial position

t = time

v0 = initial velocity

a = acceleration

If the object moves with constant speed, then a = 0 and x = x0 + v · t

If there is a collision, there will be a time "t" at which the position of Sue and the van is the same.

Let´s place the center of the frame of reference at the position of Sue when she sees the van and applies the brakes.

x Sue = x van

x0 + v0 · t + 1/2 · a · t² = x0 + v · t    (x0 Sue = 0, x0 van = 160 m)

33 m/s · t - 1/2 · 1.50 m/s² · t² = 160m + 5.20 m/s · t

33 m/s  · t - 0.75 m/s² · t² = 160m + 5.20 m/s · t

- 0.75 m/s² · t² +  27.8 m/s · t -160 m = 0

t = 7.12 s  ( the other value is t = 29.9, we take the lower one because the collision will occur only once).

The collision will occur 7.12 s from the moment Sue sees the van.

The distance traveled during that time will be:

x = x0 + v0 · t + 1/2 · a · t²

x = 33 m/s · 7.12 s - 1/2 · 1.50 m/s² · (7.12 s)²  

x = 196.9 m

The collision will occur 196.9 m inside the tunnel.