In this example we will see how a transformer can be used to change the voltage

Question

In this example we will see how a transformer can be used to change the voltage output of a wall receptacle. A friend returns from Europe with a device that she claims to be the world's greatest coffee maker. Unfortunately, it was designed to operate from a 240 V line, standard in Europe. At this rms voltage, the coffee draws 1260 W of power. (a) If your friend wants to operate the coffee maker in the United States, where the rms line voltage is 120 V , what turns ratio does her transformer need to have for the coffee maker to work? (b) What current will the coffee maker draw from the 120 V line? (c) What is the coffee maker's resistance? (These voltages and currents are rms values, so the power quantities are given by V1I1=V2I2.)

SOLUTION

SET UP Our friend needs to step up the 120 V that comes into her home to the 240 V required to operate the coffee maker, so she has to use a step-up transformer. In accord with the transformer equation, V2V1=N2N1, our friend needs a transformer with a turns ratio equal to the voltage ratio.

SOLVE Part (a): The input (primary) voltage is V1=120V, and we need an output (secondary) voltage V2=240V. The required turns ratio is

N2N1=V2V1=240V120V=2

Part (b): For a power of 1260 W , the current on the 240 V side is 5.3 A . From V1I1=V2I2, the primary current (from the 120 V source) is 11 A . The power is the same on the primary and secondary sides:

P=(120V)(11A)=(240V)(5.3A)=1260W

Part (c): For a current of 5.3 A on the 240 V side, the resistance R of the coffee maker must be

R=V2I2=240V5.3A=46

REFLECT The ratio of primary voltage to current is R'=V1/I1=120V/11A=11. The primary voltage–current relationship is the same as though we had connected a 11 resistor directly to the 120 Vsource.

Part A - Practice Problem:

Suppose we want to use the coffee maker on an airplane on which the voltage is 600 V . Find the turns ratio of the required transformer.

Express your answer as a fraction.

SubmitMy AnswersGive Up

Part B - Practice Problem:

Find the ratio R of primary voltage to current for the coffee maker on the airplane.

Express your answer in ohms to two significant figures.

In this example we will see how a transformer can be used to change the voltage output of a wall receptacle. A friend returns from Europe with a device that she claims to be the world's greatest coffee maker. Unfortunately, it was designed to operate from a 240 V line, standard in Europe. At this rms voltage, the coffee draws 1260 W of power. (a) If your friend wants to operate the coffee maker in the United States, where the rms line voltage is 120 V , what turns ratio does her transformer need to have for the coffee maker to work? (b) What current will the coffee maker draw from the 120 V line? (c) What is the coffee maker's resistance? (These voltages and currents are rms values, so the power quantities are given by V1I1=V2I2.)

SOLUTION

SET UP Our friend needs to step up the 120 V that comes into her home to the 240 V required to operate the coffee maker, so she has to use a step-up transformer. In accord with the transformer equation, V2V1=N2N1, our friend needs a transformer with a turns ratio equal to the voltage ratio.

SOLVE Part (a): The input (primary) voltage is V1=120V, and we need an output (secondary) voltage V2=240V. The required turns ratio is

N2N1=V2V1=240V120V=2

Part (b): For a power of 1260 W , the current on the 240 V side is 5.3 A . From V1I1=V2I2, the primary current (from the 120 V source) is 11 A . The power is the same on the primary and secondary sides:

P=(120V)(11A)=(240V)(5.3A)=1260W

Part (c): For a current of 5.3 A on the 240 V side, the resistance R of the coffee maker must be

R=V2I2=240V5.3A=46

REFLECT The ratio of primary voltage to current is R'=V1/I1=120V/11A=11. The primary voltage–current relationship is the same as though we had connected a 11 resistor directly to the 120 Vsource.

Part A - Practice Problem:

Suppose we want to use the coffee maker on an airplane on which the voltage is 600 V . Find the turns ratio of the required transformer.

Express your answer as a fraction.

SubmitMy AnswersGive Up

Part B - Practice Problem:

Find the ratio R of primary voltage to current for the coffee maker on the airplane.

Express your answer in ohms to two significant figures.

    

Explanation / Answer

Practice prolem
a)
V2/V1 =N2/N1
240/600 = N2/N1
N2/N1 = 0.4
N1/N2 = 2.5

b)
I dont think resistance of coffe makerwill chnage
Answer: 46 ohm

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