Question

A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B each of 24 ohms resistance, which may be used separately in series or parallel. What are the currents in three cases?

Answer 1

Hint: Using the formula for the effective resistance in series and parallel, find the effective resistance and then find the value of the current using the ohm's law, which states that the value of the current is equal to the ratio of the voltage and the effective resistance .

Step by step solution:

The problem can be solved in three cases

Case 1: When the resistances are used separately
Here the value of the resistance is given as 24 ohms
So the effective resistance when the resistance is used separately becomes the same as the given resistance.
So we have now the value of the resistance as 24 ohms. Now we can find the value of the current using the ohm's law as below :
The ohm's law can be stated as the voltage in the circuit is equal to the product of the resistance and the value of the current across the branch
Now the value of the current becomes $I = \dfrac{V}{R} = \dfrac{220}{24} = 9.16 A $
The value of the current when the resistance is used separately is 9.16 amperes

Case 2: When the resistance is connected in series connection :
We get the value of the resistance in series connection as :
$R_{eq} = R_1 + R_2$
The value of the resistance we have is 24 ohms
The value of the resistance when we use the series connection becomes as $R_eq = 24 +24 = 48 $
So the value the current in case of the series connection becomes using the ohm's law as $I = \dfrac{220}{48} = 4.58 A $
The value of the current in the case of series connection is found as: 4.58 amperes

Case 3: The resistance is arranged in a parallel connection.
The value of the resistance in the parallel connection is given by :
$R_eq = \dfrac{R_1 R_2}{R_1 + R_2} $
So substituting the given resistance we get the effective resistance in parallel connection becomes $R_eq = \dfrac{24 \times 24}{24+24} = 12 $ ohms
The current in the circuit becomes : $I = \dfrac{220}{12} = 18.33 A $

The value of the currents in this case is found as 18.33 A

Note: We can observe the value of the current depends on the effective resistance between the lines. The current observed is lesser in case of the series resistance as the value of the resistance in case of the series resistance is higher.
Be careful while calculating resistance for parallel connection. Effective resistance for parallel connection is always lesser than individual resistances.