Answer:
a) see attached
b) 15015 meters
Explanation:
You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.
Voltage and current laws
The relevant circuit relations are ...
- Kirchoff's voltage law: the sum of voltages around a loop is zero
- Kirchoff's current law: the sum of currents into a node is zero
- Ohm's law: voltage is the product of current and resistance
- Series: elements in series have the same current
- Parallel: elements in parallel have the same voltage
Voltage
Given current and resistance for element 1, we immediately know its voltage is ...
V = IR = (4)(10) = 40 . . . . volts
Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.
Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...
90 -(40 +30) = 20
Current
The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.
That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...
4 - 1 = 3 . . . . amperes
Resistance
The resistance of each element is the ratio of voltage to current:
R = V/I
Dividing the V column by the I column gives the values in the R column.
Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.
Power
Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.
Note that the power supplied by the source T is the sum of the powers in the load elements.
b) Wavelength
We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...
(90 W)×(222 Hz/W) = 19980 Hz
Then the wavelength is ...
λ = c/f
λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle
The wavelength of the broadcast is about 15015 meters.
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Additional comment
The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."
Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).
Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.
As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).
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