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Zorluk: Çok zorSeries Circuits

During the calibration of a naval radar control system, engineers measure a continuous current of 1.5 A1.5\text{ A} flowing through a series safety loop. The loop is energized by a 60 V60\text{ V} direct current source and contains three elements: a 15 Ω15\ \Omega current-limiting resistor (R1R_1), a calibration rheostat (R2R_2), and a primary sensor coil (R3R_3). If the primary sensor coil dissipates exactly 36 W36\text{ W} of power, what is the required resistance of the calibration rheostat (R2R_2)?

  1. A
    1 Ω1\ \Omega
  2. B
    40 Ω40\ \Omega
  3. 9 Ω9\ \OmegaCevap
  4. D
    59 Ω59\ \Omega

Cevap

The required resistance of the calibration rheostat is 9 Ω9\ \Omega.
In this series circuit, the total resistance must equal the source voltage divided by the total current (60 V/1.5 A=40 Ω60\text{ V} / 1.5\text{ A} = 40\ \Omega). Since components are in series, they share the same 1.5 A1.5\text{ A} current. The sensor coil dissipates 36 W36\text{ W}, meaning its resistance is P/I2P / I^2 (36/2.25=16 Ω36 / 2.25 = 16\ \Omega). Subtracting the 15 Ω15\ \Omega resistor and the 16 Ω16\ \Omega coil from the 40 Ω40\ \Omega total leaves 9 Ω9\ \Omega for the calibration rheostat.

Adım Adım Çözüm

1
Calculate the total equivalent resistance of the series circuit using Ohm's Law.
RT=VTIT=60 V1.5 A=40 ΩR_T = \frac{V_T}{I_T} = \frac{60\text{ V}}{1.5\text{ A}} = 40\ \Omega
Total resistance is needed to find the missing component value in a series string.
2
Determine the resistance of the primary sensor coil (R3R_3) using the power formula P=I2RP = I^2R.
R3=PI2=36 W(1.5 A)2=362.25=16 ΩR_3 = \frac{P}{I^2} = \frac{36\text{ W}}{(1.5\text{ A})^2} = \frac{36}{2.25} = 16\ \Omega
Since the circuit is in series, the full 1.5 A1.5\text{ A} current flows through all components, allowing the coil's resistance to be calculated from its power dissipation.
3
Subtract the known series resistances from the total resistance to find the rheostat's value (R2R_2).
R2=RT−R1−R3=40 Ω−15 Ω−16 Ω=9 ΩR_2 = R_T - R_1 - R_3 = 40\ \Omega - 15\ \Omega - 16\ \Omega = 9\ \Omega
In a series circuit, total resistance is the sum of all individual resistances (RT=R1+R2+R3R_T = R_1 + R_2 + R_3).

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