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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 $$\Omega$$resistances, which may be used separately, in series, or in parallel. What are the currents in the three cases?

Supply voltage, V= 220 V
Resistance of one coil, R= 24 $$\Omega$$

(i) Coils are used separately
According to Ohm's law,
$$V= I_1R_1$$
Where, $$I_1$$ is the current flowing through the coil

$$I_1 = \frac{V}{R_1} = \frac{220}{24} = 9.166 A$$

Therefore, 9.16 A current will flow through the coil when used separately.

(ii) Coils are connected in series

Total resistance, $$R_2$$ = 24 $$\Omega$$ + 24 $$\Omega$$ = 48 $$\Omega$$

According to Ohm's law,V = $$I_2R_2$$

Where, $$I_2$$ is the current flowing through the series circuit

$$I_2 = \frac{V}{R_2} = \frac{220}{48} = 4.58 A$$

Therefore, 4.58 A current will flow through the circuit when the coils are connected in series.

(iii) Coils are connected in parallel

Total resistance, R3 is given as $$= \frac{24}{2} = 12V$$

According to Ohm's law,
$$V= I_3R_3$$
Where,

I3 is the current flowing through the circuit $$I_3 = \frac{V}{R_3} = \frac{220}{12}= 18.33 A$$

Therefore, 18.33 A current will flow through the circuit when coils are connected in parallel.