Suppose there are two transformers between your house and the high-voltage transmission line that distributes the power. In addition, assume your house is the only one using electric power. At a substation the primary of a step-down transformer (turns ratio = 1:25) receives the voltage from the high-voltage transmission line. Because of your usage, a current of 67.5 mA exists in the primary of the transformer. The secondary is connected to the primary of another step-down transformer (turns ratio = 1:39) somewhere near your house, perhaps up on a telephone pole. The secondary of this transformer delivers a 240-V emf to your house. How much power is your house using? Remember that the current and voltage given in this problem are rms values.

Io2 = 67.5mA * 25 * 39 = 65,812.5 mA = 65.81 A.= Output current of T2.

Po2=Vo2 * Io2=240 * 65.81=15,795 Watts =
Power output of T2 = Power used by home.

To find the power used by the house, we need to calculate the current flowing through the secondary of the second transformer.

First, let's find the current in the secondary of the first transformer using the turns ratio:

Turns ratio of the first transformer = 1:25

Current in the primary of the first transformer = 67.5 mA = 67.5 * 10^(-3) A

Since the turns ratio is 1:25, the current in the secondary of the first transformer is:

Current in the secondary of the first transformer = Current in the primary of the first transformer * (1/25) = 67.5 * 10^(-3) A * (1/25) = 2.7 * 10^(-3) A

Now, let's find the current in the primary of the second transformer using the turns ratio:

Turns ratio of the second transformer = 1:39

Current in the secondary of the first transformer = 2.7 * 10^(-3) A

Since the turns ratio is 1:39, the current in the primary of the second transformer is:

Current in the primary of the second transformer = Current in the secondary of the first transformer * (1/39) = 2.7 * 10^(-3) A * (1/39) = 6.92 * 10^(-5) A

Finally, let's find the power used by the house using the current and voltage in the secondary of the second transformer:

Voltage in the secondary of the second transformer = 240 V

Current in the primary of the second transformer = 6.92 * 10^(-5) A

Power used by the house = Voltage * Current = 240 V * 6.92 * 10^(-5) A ≈ 0.0166 W

Therefore, the power used by the house is approximately 0.0166 W.

To find the power used by your house, you need to calculate the power at each stage of the transformers and then multiply them together.

First, let's find the power at the primary of the first transformer. The current through the primary (Ip1) is given as 67.5 mA. Remember that this is the rms (root mean square) value of the current. To calculate the power (Pp1) at the primary, use the formula:

Pp1 = Ip1^2 * Rp1,

where Rp1 is the resistance of the primary coil. Since the problem doesn't provide the resistance, we'll assume it to be negligible (usually, transformers have very low resistances).

Next, we need to find the power at the secondary of the first transformer. The turns ratio (N1:N2) is given as 1:25. To find the current at the secondary (Is1), use the formula:

Is1 = Ip1 * (N1/N2),

where N1 is the number of turns in the primary coil and N2 is the number of turns in the secondary coil. The power (Ps1) at the secondary is given by:

Ps1 = Is1^2 * Rs1,

where Rs1 is the resistance of the secondary coil (again, considering it to be negligible).

Now, let's move on to the second transformer. The secondary of the first transformer is connected to the primary of the second transformer with a turns ratio of 1:39. The current at the primary of the second transformer (Ip2) is equal to the current at the secondary of the first transformer (Is1). Therefore, Ip2 = Is1.

Finally, we can calculate the power at the secondary of the second transformer (your house). The turns ratio (N3:N4) is given as 1:1, meaning there is no voltage change. The voltage at the secondary (Vs2) is given as 240 V (rms), so we can directly calculate the power (Ps2) as:

Ps2 = Vs2^2 / Rs2,

where Rs2 is the resistance of your house (again, assuming it to be negligible compared to the load).

To find the total power used by your house, multiply all the calculated powers together:

Total power = Pp1 * Ps1 * Ps2.

Remember to convert the current to Ampere (A) and voltage to Volt (V), if necessary, before making the calculations.