Question

The diagram below shows a "galvanometer", which can be used as a simple ammeter. Its various pieces are:

The coil:
A circular coil of total resistance 1 Ω is made from 2000 turns, each approximately of radius r = 50 mm. This coil (in red) is wound around a spherical support (gray) which has an attached needle. All of these pieces stay fixed relative to each other.

The spring:
The coil/support/needle system is mounted on an axle which can swivel, but is attached to a circular spring. The spring is at its equilibrium when the needle is pointed vertically, but otherwise pulls back towards this equilibrium (in proportion to how far it is taken away from it). Assume the spring obeys the rotational version of Hooke's Law (F_sp= kΔx) with a restoring torque of size τ = kϕ (where the spring constant k = 0.005 N·m/deg).

The field:
The coil sits in a magnetic field created by two bar magnets. You may take this field to be uniform with size B=300 mT and pointing to the right (from "N" to "S".)



a.) Examine the diagram above carefully, and then answer the question below (for the direction of current depicted):

The loop's normal vector points  ---Select--- in the same direction as in the opposite direction as perpendicularly to the ammeter needle.

b.) If the needle moves to ϕ = 13^o, how much current is passing through the ammeter?
mA
This number should be painted onto your ammeter dial-- whenever the needle is here, this is the current.

c.) Now that you understand the general operation principle of an ammeter, let's use it in a circuit.

Suppose you connect a 410 Ω resistor to a ε = 9 V battery.

How much current would flow through the resistor, if the ammeter is not included yet?  mA

Assuming you wanted to try to measure that current, how much will the ammeter's inclusion in the circuit affect this very current you are trying to unobtrusively measure?
(Neglect any other resistance besides the resistor and the ammeter coil.)

---Select--- increase decrease it by  mA.
Does this seem like a large measurement error?

d.) Suppose the wire used to make the ammeter coil has a cross-sectional radius r_w = 0.2 mm. What is the resistivity of the material the wire is made from? (Neglect temperature dependent effects.)

ρ_o =  Ω·m

Answer 1