A hot plate of an electric oven connected to a $220\ V$ line has two resistance coils A and B, each of $24\ Ω$ resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?
Given: A hot plate of electric oven connected with 220 V has two resistance coils A and B each of 24 Ω.
Here, $V=220\ V$
$R_1=24\ Ω$
$R_2=24\ Ω$
To do: To calculate the current in three cases when the two resistance coils A and B are used separately, in series, or in parallel.
Solution:
Case 1: Resistance coils used separately$\Rightarrow$
Here, $V=220\ V$
$R=24\ Ω$
Therefore, the current flowing $I=\frac{V}{R}$
$=\frac{220\ V}{24\ Ω}$
$=9.167\ A$
Case 2: Resistance coils used in series$\Rightarrow$
When the resistance coils are used in series, then $R_{eq}=R_1+R_2$
$=24\ Ω+24\ Ω$
$=48\ Ω$
Therefore, current flowing $I=\frac{V}{R_{eq}}$
$=\frac{220\ V}{48\ Ω}$
$=4.583\ A$
Case 3: Resistance coils are used in parallel$\Rightarrow$
When the resistance coils are used in parallel, then
$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$
Or $\frac{1}{R_{eq}}=\frac{1}{24\ Ω}+\frac{1}{24\ Ω}$
Or $\frac{1}{R_{eq}}=\frac{2}{24\ Ω}$
Or $\frac{1}{R_{eq}}=\frac{1}{12\ Ω}$
Or $R_{eq}=12\ Ω$
Therefore, current flowing $I=\frac{V}{R_{eq}}$
$=\frac{220\ V}{12\ Ω}$
$=18.334\ A$
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