PHYsics 1161

Hour Exam #2

March 3, 2003

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You may have one sheet of equations (one side of an ordinary 8.5 x 11 inch sheet
of paper).

As always, **show your work**. Please don’t leave me guessing or trying
to read your mind. My ESP skills are very poor!

1. An electron moves in a circular path, perpendicular to a magnetic field of B = 1.25 T, with a a speed of 1.2 x 10

Alternatively, we could have solved it symbolically first, as here,

2. A rectangular loop has dimensions of 2.0 cm (0.02 m) by 3.0 cm (0.03 m) and is initially between the poles of a large magnet, where the magnetic field strength is B = 0.050 T. The loop is oriented so the normal to the plane of the coil lies parallel to the direction of the magnetic field. The coil is removed from that region to a region with no magnetic field in 0.15 seconds. What is the average induced emf?

3. An electric light bulb, connected to an ordinary 120 V AC wall outlet, uses 60 W of power. What are

a) the rms

b) the maximum and minimum instantaneous values of the

c) the maximum and minimum instantaneous values of the

d) the

4. Consider a series RCL circuit with R = 80 W, C = 250 µF, L = 250 mH connected to a 12 V, 120 Hz AC source.

a), b) What are the

c) What is the total

d) What

e) What is the

5.

i. A loop of wire is perpendicular to a magnetic field as shown in the sketch below. The magnetic field is initially directed

What is the direction of the induced current in the loop of wire?

clockwise?

**counterclockwise?**

**Explain** your answer!

We **began** with magnetic flux pointing **out of** the page and **ended** with flux pointing **into** the page. The **induced magnetic field** will try to **restore** the change in the flux -- or restore the flux to its initial condition. That means the **induced magnetic field** will point **out of** the page. The **induced electric current** that **causes** this **induced magnetic field** must be **counterclockwise**, according to the right hand rule.

ii. Explain the minus sign in Lenz’ Law.

The minus sign simply says the **direction** of the **induced** **emf** is such that the corresponding **induced magnetic field** will **oppose the change** in the magnetic flux.

iii. Will the current in an AC series RC circuit increase or decrease when the frequency of the AC source ** increases**?

The current through a capacitor in a DC circuit is

Mathematically, we can see this from

X_{C} = ^{1}/_{( 2
f C)}

As f increases, X_{C} **de**creases. X_{C}, the “capacitave
reactance” is much like a resistance. A **de**crease in X_{C}
means an **in**crease in the current I.

Consider the following circuits. The three batteries are identical. The five light bulbs are identical. The power absorbed by a light bulb is directly related to its brightness.

iv. Rank the five light bulbs in order of their **brightness** (or power). Some bulbs may be equally bright.

A = D =
E > B = C

The **same voltage** that is across A is also acros
D and E. So the brightness -- or the power or the current -- of all three of
these must be the **same**.

The voltage across B is the same as the voltage across C so the brighteness
of B and C must be the same. The voltage across **both** B and C in series
is the same as the voltage across A so the current through B and C will be less
than the current through A; the brightness of B or C will be less than the brightness
of B.

v. Rank the **current** through the three batteries.

This asks for the current through the batteries so it
is a question of 1, 2, 3 or I_{1}, I_{2}, and I_{3}.
It is **not** a questions to be answered with A, B, C, D, and E.

Bulbs D and E have the **same voltage** across each or either of them as
the voltage across A. So they **each** have the same current as that through
bulb A. That means the current through battery 3 must be **twice** the current
through battery 1. That is,

I_{3} > I_{1}

The equivalent resistance for battery 2 is **twice**
the resistance for battery 1 so the current supplied by battery 2 will be **one
half** that supplied by battery 1. That is,

I_{1} > I_{2}

Putting these together, we have

I_{3} > I_{1} > I_{2}

vi. **Bonus Question**

Citroen DS21 was a French automobile.

(Not much “Physics” in this one. It was meant only as a fun question
for students who were in class on Friday.