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# A hot plate of an electric oven connected to a $220\ V$ line has two resistance coils A and B, each of $24\ â„¦$ 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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