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Calculate the efficiency of the transformer using the provided power and current values.

Physics

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97.

  1. Calculate the total output power of the light bulbs.

    The transformer lights up four 12 V, 24 W light bulbs.
    Total output power (PoutP_{out}) = Number of bulbs ×\times Power per bulb

    Pout=4×24 WP_{out} = 4 \times 24 \, \text{W} Pout=96 WP_{out} = 96 \, \text{W}
  2. Determine the input power to the transformer.

    From , the transformer takes 0.55 A0.55 \, \text{A} from a 240 V240 \, \text{V} mains. This is the input power (PinP_{in}).

    Pin=Vmains×ImainsP_{in} = V_{mains} \times I_{mains} Pin=240 V×0.55 AP_{in} = 240 \, \text{V} \times 0.55 \, \text{A} Pin=132 WP_{in} = 132 \, \text{W}
  3. Calculate the efficiency of the transformer.

    Efficiency (η\eta) is the ratio of output power to input power, expressed as a percentage.

    η=PoutPin×100%\eta = \frac{P_{out}}{P_{in}} \times 100\% η=96 W132 W×100%\eta = \frac{96 \, \text{W}}{132 \, \text{W}} \times 100\% η≈0.727272×100%\eta \approx 0.727272 \times 100\% η≈72.73%\eta \approx 72.73\%

    The efficiency of the transformer is 72.73%\boxed{\text{72.73\%}}.

    98.

  4. Identify the given input voltage and input current.

    The transformer supplies 12 V12 \, \text{V} (output) from a 240 V240 \, \text{V} mains (input voltage, VpV_p).
    It takes 0.55 A0.55 \, \text{A} from the mains (input current, IpI_p).

  5. Calculate the power delivered to the transformer (input power).

    The power delivered to the transformer (PinP_{in}) is the product of the input voltage and input current.

    Pin=Vp×IpP_{in} = V_p \times I_p Pin=240 V×0.55 AP_{in} = 240 \, \text{V} \times 0.55 \, \text{A} Pin=132 WP_{in} = 132 \, \text{W}

    The power delivered to the transformer is 132 W\boxed{\text{132 W}}.

    99.

  6. Identify the given values.

    Resistance of the cable (RR) = 0.5 Ω0.5 \, \Omega.
    Electricity generated (PgenP_{gen}) = 11 kW=11000 W11 \, \text{kW} = 11000 \, \text{W}.
    Transmission voltage (VV) = 120 V120 \, \text{V}.

  7. Calculate the current flowing through the cable during transmission.

    The current (II) can be found using the formula P=VIP = V I.

    I=PgenVI = \frac{P_{gen}}{V} I=11000 W120 VI = \frac{11000 \, \text{W}}{120 \, \text{V}} I≈91.6667 AI \approx 91.6667 \, \text{A}
  8. Calculate the power wasted in the cable.

    The power wasted (PwastedP_{wasted}) due to the resistance of the cable is given by Pwasted=I2RP_{wasted} = I^2 R.

    Pwasted=(91.6667 A)2×0.5 ΩP_{wasted} = (91.6667 \, \text{A})^2 \times 0.5 \, \Omega Pwasted=8402.78×0.5 WP_{wasted} = 8402.78 \times 0.5 \, \text{W} Pwasted=4201.39 WP_{wasted} = 4201.39 \, \text{W}

    To express in kilowatts:

    Pwasted=4201.391000 kWP_{wasted} = \frac{4201.39}{1000} \, \text{kW} Pwasted≈4.20 kWP_{wasted} \approx 4.20 \, \text{kW}

    The power wasted in the cable is 4.20 kW\boxed{\text{4.20 kW}}.

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