Question

Resistances of 40 ohm and 60 ohm are connected in series across a 200 V battery. find the heat in calories produced by the combination in 1/2 minute.

Ans : 2870 calories

Answer 1

In series combination
R = 40 + 60 = 100 Ohm

Power = V^2 / R
= (200)^2 / 100
= 40 Watt

Energy = Power * Time
= 400 Watt * 30 seconds
= 12000 Joules
= (12000 / 4.180) cal
= 2870 cal

Answer 2

Given,

Resistances of 2 resistors connected in series = 40 ohms and 60 ohms

Voltage supply across the resistors = 200 V

To find,

The heat in calories produced by the combination in 1/2 minutes.

Solution,

We can simply solve this numerical problem by using the following process:

Mathematically,

If a set of resistors are arranged in a series type of arrangement, then the equivalent resistance of the arrangement is equal to the total of the individual resistances. The voltage supply across each resistance is equal to the voltage supply across the resistor.

{Statement-1}

As per ohms law,

For a voltage V across the conductor, current I flowing through the conductor and resistance R provided by the conductor to the flow of current, V = RI.{Statement-2}

Mathematically, according to Joule's law,

The amount of heat produced by a resistor (H) = (current)^2×(resistance)×(time)

{Statement-3}

Now, according to statement-1;

The equivalent resistance of the circuit

= sum of individual resistances in series arrangement

= 40 ohms + 60 ohms

= 100 ohms

Now, according to the statement-2;

The total current flowing through the circuit

= (total voltage supply across the resistor)/(total resistance of the circuit)

= 200 V/100 ohms

= 2 A

Now, according to the statement-1;

2A current flows through both the resistors of the circuit.

Now, according to the statement-3;

The total heat in calories produced by the combination in 1/2 minute

= (total heat in calories produced by the 60 ohms resistor in 30 seconds) + (total heat in calories produced by the 40 ohms resistor in 30 seconds)

= (current flowing through the 60 ohms resistor)^2×(resistance of the 60 ohms resistor)×(time) + (current flowing through the 40 ohms resistor)^2×(resistance of the 40 ohms resistor)×(time)

= (total current flowing through both the resistors)^2×( equivalent resistance of the combination)×(time)

= (2A)^2×(100 ohms)×(30 s)

= 12000 Joules

= (12000/4.2) Cal

(12000/4.2) Cal{Since 1 J = 1/4.18 Cal}

= 2870 Cal

Hence, the total heat in calories produced by the combination in 1/2 minute is equal to 2870 Cal.