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Question

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


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Solution

Step1: Given data-

Voltage V=220V

Resistance of coil A(R1)=24Ω

Resistance of coil B(R2)=24Ω

Step 2: Formula used

V=IR

Step 3: Calculating the currents in different situations:

Case A: If resistance is used, individual

Let I1 be the current when resistance used separately.

According to ohm's law V=I1R1 (V=Voltage.I=current.R=Resistance)

I1=VR1=22024=9.166A

Case B: If resistances are in series

Let Reqbe the equivalent resistance in series and I2 be the current when resistances are connected in series. Req=R1+R2=24+24=48Ω

According to ohm's law V=I2Req (V=Voltage.I=current.R=Equivalent Resistance) V=I2ReqI2=VReq=22048=4.58A

Case C: If resistances are in parallel

Let Req2be the equivalent resistance in parallel and I3 be the current when resistances are connected in parallel. 1Req2=1R1+1R21Req2=124+1241Req2=2241Req2=112

Req2=12Ω

According to ohm's law V=I3Req2 (V=Voltage.I=current.R=Equivalent Resistance) I3=VR=22012=18.33A

Thus, I1=9.166AI2=4.58AI3=18.33A.


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