Electricity Worksheet21

A given wire is stretched to double its length. How will its resistance change ?

A wire of 3 Ω a resistance and 10 cm length is stretched to 30 cm length. Assuming that it has uniform crosssection, what will be its new resistance ?

A rheostat and a resistance box are both used to change current in a circuit. In what respect the two differ from each other?

How do we symbolically represent a connecting wire and a resistor ? What is the significance of the symbol of a resistor ?

What sets the electrons into motion in an electric circuit ?

Tap water conducts electricity whereas distilled water does not. Why ?

Graphs between electric current and potential difference across two conductors A and B are as shown in the figure. Which of the two conductors has more resistance?

The electrical resistivity of a few materials are given in ohmmetre. Which of these materials can be used for making an element of a heating device ?
(A) 6.84 × 10^{–8} (B) 1.60 ×10^{–8}
(C) 1.00 × 10^{–4} (D) 2.50 × 10^{12}
(E) 4.40 × 10^{–5} (F) 2.30 × 10^{17}

Two wires A and B are of equal lengths, different crosssectional areas and made of the same metal. Name the property which is same for both the wires and which is different for both the wires.
if the resistance of wire A is four times the resistance of wire B, calculate The ratio of the crosssectional areas of the wires and the ratio of the radii of the wires.

Two metallic wires A and B are connected in parallel. Wire A has length l and radius r, wires B has a length 2 l and radius 2 r. Compute the ratio of the total resistance of the parallel combination and the resistance of wire A.
Answer:

Suppose the original length of the wire is I and its crosssectional area is A, then its resistance, R = Pl/A. When the length is doubled to 2 l, crosssectional area reduces to A/2 because volume of the wire does not change.
So the changed resistance,

When the length of the wire becomes three times (from 10 cm and 30 cm), its area of crosssection is reduced from A to A/3. Therefore, new resistance,

The change in resistance in a rheostat is unknown whereas in the resistance box it is known.

A connecting wire and a resistor are represented as shown in
A straight line symbol for a connecting wire means that it offers no resistance to the flow of electrons. The hills () in case of a resistor represent the obstruction to the flow of electrons.

To set the electrons into motion in an electric circuit, a cell or a battery is used which provides potential difference across its terminals.

Electricity is conducted through liquids by ions. Tap water conducts electricity due to presence of ions of dissolved salts and minerals in it. But distilled water which is a covalent compound has no ions to conduct electricity through it.

It is clear from the graphs A and B, for a given pd, i.e., V, the current through the conductor A (i.e., I_{A}) is less than the current through conductor B (i.e., I_{B}) i.e. I_{A} < I_{B}. Since for a given value of V.
Since I_{A} < I_{B}, R_{A} > R_{B}, i.e., conductor A has more resistance than the conductor B.

For making the element of a heating device, we use an alloy because :
(i) its resistivity changes less rapidly with changes in temperature
(ii) it does not oxidize or burn readily at high temperature.
From the table,
The resistivity of materials C and E lie in the range of resistivity of alloys. So they can be used for this purpose.

Resistivity. The resistivity is the property of the material of which the wire is made. Since both the wires are made of the same metal, their resistivity will be same.
Resistance. As both the wires are of different crosssectional areas, their resistances are different as (R ∝ 1/A)
For wire A, and for wire B,
Since R_{1} = 4R_{2}, Thus,
(ii) A_{1} = πr_{1}^{2} and A_{2} = πr_{2}^{2},
or

Since both the wires A and B are of the same material, their resistivity will be same, i.e. p.
Resistance of the wire A, i.e.,
Resistance of the wire B, i.e.,
Total resistance of the parallel combination, i.e., R_{p} is given by
or
Clearly,