[3 Mark Questions]

Question 13 Marks

A current of 1 ampere flows in a series circuit containing an electric lamp and a conductor of 5Ω when connected to a 10V battery. Calculate the resistance of the electric lamp.
Now if a resistance of 10Ω is connected in parallel with this series combination, what change (if any) in current flowing through 5Ω conductor and potential difference across the lamp will take place? Give reason.

Answer

Total resistance of circuit can be calculated as follows:$\text{R}=\frac{\text{V}}{\text{I}}=\frac{10\text{V}}{1\text{A}}=10\Omega$
Since lamp and conductor are in series so resistance of lamp,
$=10\Omega-5\Omega=5\Omega$
The new resistance in parallel to earlier combination has same value, i.e. 10Ω as the resistance of series combination. This means that the amount of current would be equally divided into two branches. Hence, 0.5A current will flow through 5Ω conductor.
Now, resistance remains the same but current has become half. Using Ohm formula, potential difference across the lamp can be calculated as follows:$\text{V}=\text{IR}=0.5\text{A}\times5\Omega=2.5\text{V}$

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Question 23 Marks

Draw a circuit diagram of an electric circuit containing a cell, a key, an ammeter, a resistor of 2Ω in series with a combination of two resistors (4Ω each) in parallel and a voltmeter across the parallel combination. Will the potential difference across the 2Ω resistor be the same as that across the parallel combination of 4Ω resistors? Give reason.

Answer

Equivalent resistance of two resistors (4Ω each) connected in parallel is given by
$\frac{1}{\text{R}}=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\text{ or R}=2\Omega$
Therefore, the above circuit can be redrawn as given below:

Therefore, potential difference across 2Ω resistor will be same; as that of across the parallel combination of 4Ω resistors. V = IR.
As R and I in both the cases is same so V = same.

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Question 33 Marks

What is electrical resistivity? In a series electrical circuit comprising a resistor made up of a metallic wire, the ammeter reads 5A. The reading of the ammeter decreases to half when the length of the wire is doubled. Why?

Answer

The inherent property of a conductor because of which it resists the flow of electric current is called resistivity. Resistivity for a particular material is unique.
Resistance varies directly as length of the conductor.
Current varies inversely as resistance.
So, when length of the wire is doubled, its resistance becomes double. When resistance becomes double, current becomes half.
This explains why the reading of ammeter decreases to half when the length of the wire is doubled.

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Question 43 Marks

Why is parallel arrangement used in domestic wiring?

Answer

Parallel arrangement is used in domestic wiring due to the following reasons:

Each device will have the same voltage which is equal to the voltage of the supply.
If two or more devices are used at the same time then, each appliance will be able to draw the required current.
If one of the devices fails then other keeps working.

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