Chapter 11 : Electricity

Previous Years Questions 2008

Question: Out of 60 W and 40 W lamps, which one has a higher electrical resistance when in use ? [1M]

Solution: We know that , 

  

For the 60 W lamp:

For the 40 W lamp: 

Since 40 < 60, the denominator in the resistance calculation for the 40 W lamp is smaller, leading to a larger resistance.

Question: Why are the coils of electric toasters made of an alloy rather than a pure metal ? [2M]

Answer : The coils of electric toasters are made of an alloy because alloys have higher resistivity and melting points than pure metals, ensuring efficient heat generation without melting. They are also less prone to oxidation at high temperatures, providing durability and consistent performance.

Question: Two lamps, one rated 60 W at 220 V and the other 40 W at 220 V are connected in parallel to the electric supply at 220 V .[3M]

(a) Draw a circuit diagram to show the connections .

(b) Calculate the current drawn from the electric Supply .

(c) Calculate the total energy consumed by the two lamps together when they operate for one hour .

Solution: (a) The circuit diagram of two lamps :

 

(b)  For the 60 W lamp : Here, ,

We have ,  

For the 40 W lamp : Here, ,

We have , 

 

(c)  Here,  ,  

We have,   

Previous Years Questions 2009

Question: A piece of wire of resistance 20 Ω is drawn out so that its length is increased to twice its origin length . calculate the resistance of the wire the new situation . [2M]

Solution:  Here,   and

When a wire is stretched to twice its original length, the resistance of the wire changes because resistance depends on the length and cross-sectional area of the wire.

We have,  

The resistance of the wire the new situation : 

A/Q,      

 

Question: Two resistor , with resistance 5 and 10 respectively are to be connected to abattery of emf 6V so as to obtain :

(a) How will you connect  the resistance in each case ?

(i) Minimum current flowing

(ii) Maximum current flowing

(b) Calculate the strength of the total current in the circuit in the two cases . [3M]

Solution:  (a) Here,

(b) Here,

 

(c) For series Connection :

We have,  

For series Connection :

We have,  

Previous Years Questions 2010

Question: Derive the expression for the heat produced due to a current  flowing for a time interval  through a resistor R having a potential difference V across it ends . With which name is the relation known ? How much heat will an instrument of 12 W produce in one minute if it is connected to a battery of 12 V ? [5M]

Answer : A current  flows through a resistor of resistance . Let the potential difference across it be , and let  be the time during which a charge  flows through it. The work done in moving the charge  across the potential difference  is . Therefore, the source must supply energy equal to  in the time . Hence the power input to thje circuit by the sources is

Using Ohm's Law : 

 

The total heat energy  produced is the power multiplied by the time :

This relationship is known as Joule's Law of Heating.

Given: Power , ; Time,  minute = 60 second

We have, J

Question:  Explain with the help of a labeled circuit diagram how you will find the resistance of a combination of three resistor, of resistance R1 , R2 and R3 joined in parallel. Also, mention how you will connect the ammeter and the voltmeter in the circuit and the potential difference across one of the three resistors of the combination . [5M]

Answer:  We consider a parallel combination,  of three resistors having resistances and , respectively.

Connect it with a battery , a plug key and ammeter and also connect a voltmeter in parallel with combination of resistors. Let  be the total current .The total current , is equal to the sum of the separate currents through each branch of the combination.

Let  be the equivalent resistance of the parallel combination of resistors. By applying Ohm’s law to the parallel combination of resistors, we have

 

On apply ohm’s law to each resistor, We have

  ;    ;

From (i) we get,

Ammeter: Must be connected in series to measure the total current flowing through the circuit.

Voltmeter: Must be connected in parallel to measure the voltage across the resistor combination.

Resistor Voltages: Since the resistors are in parallel, the voltage across each resistor is equal to the total voltage V.