Question

An electric tea kettle has two electric heating coils. When one of the coils is switched on the tea begins to boil in $6$ minutes. When the other is switched on, the boiling begins in $8$ minutes If both the coils are now arranged in series and switched on, boiling starts in
A. $\dfrac{{24}}{7}$ minutes
B. $12$ minutes
C. $14$ minutes
D. $4$ minutes

Answer 1

Hint: Students should know what resistance is and how it is related to the temperature formula for resistance. Formula for resistance when it is kept in series connection and ohm’s law. Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference applied across its ends, provided the temperature and other physical conditions remain unchanged.

Complete step by step answer:
The device which allows us to introduce a controlled amount of resistance into an electrical circuit is known as a resistor. Current is directly proportional to voltage difference through a resistor. That is, if the current doubles, then so does the voltage. To make a current flow through a resistance there must be a voltage across that resistance. Ohm's Law shows the relationship between the voltage (V), current (I) and resistance (R)
$I\propto V$ or $V\propto I$
$ \Rightarrow V = IR$
Where R is a constant called resistance of the conductor. The value of this constant depends on the nature, length, area of cross section and temperature of the conductor.

As per the ohm’s law we have,
$V = IR$
Were, $R = \rho \dfrac{l}{a} - - - - (1)$
Here, $\rho $ is the resistivity ‘l’ is the length of material and ‘a’ is the area of the material.
And here the length and area of the cross section is affected by temperature.As temperature increases resistivity increases. So therefore, as resistance is directly proportional to resistivity as resistivity increases resistance also increases with temperature.Resistance in series combination,
${R_{eq}} = {R_1} + {R_2} + {R_3} + {R_4} + ... + {R_n}$
Therefore, ${T_1} = 6\min {\text{ and }}{T_2} = 8\min $
${T_{eq}} = {T_1} + {T_2}$
$ \Rightarrow {T_{eq}} = 6 + 8$
From the above equation, ${T_{eq}}$ in series is equal to
$ \therefore {T_{eq}} = 14\min $

Therefore, the correct answer is option C.

Note: For ohm’s law it is a necessary condition that the temperature must be constant. It’s true only for linear electrical elements. For non-linear electrical elements with parameters like capacitance, resistance etc, the voltage and current won’t be constant with respect to time making it difficult to use Ohm’s law. Ohm’s law is not applicable for unilateral electrical elements like diodes and transistors as they allow the current to flow through in one direction only.