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Indicate whether the following statements are TRUE or FALSE by writing only 'True' or 'False' next to the question number (1.1.1–1.1.3) in the ANSWER BOOK.

Physics

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Answer

120.48∠1.95∘Ω\text{120.48} \angle 1.95^\circ \Omega

Step-by-step solution

3 steps
  1. Identify the given total voltage and total current.

    The total voltage across the circuit is VT=100∠0∘ VV_T = 100 \angle 0^\circ \text{ V}.
    The total current flowing through the circuit is IT=0.83∠−1.95∘ AI_T = 0.83 \angle -1.95^\circ \text{ A}.

  2. Apply Ohm's Law for AC circuits to calculate the total impedance.

    The total impedance ZTZ_T is given by the ratio of the total voltage to the total current:

    ZT=VTITZ_T = \frac{V_T}{I_T}
  3. Substitute the given values and perform the calculation.

    To divide complex numbers in polar form, divide their magnitudes and subtract their angles.

    ZT=100∠0∘ V0.83∠−1.95∘ AZ_T = \frac{100 \angle 0^\circ \text{ V}}{0.83 \angle -1.95^\circ \text{ A}} ZT=(1000.83)∠(0∘−(−1.95∘))ΩZ_T = \left(\frac{100}{0.83}\right) \angle (0^\circ - (-1.95^\circ)) \Omega ZT=120.48∠(0∘+1.95∘)ΩZ_T = 120.48 \angle (0^\circ + 1.95^\circ) \Omega ZT=120.48∠1.95∘ΩZ_T = 120.48 \angle 1.95^\circ \Omega

    The total impedance of the circuit is 120.48∠1.95∘Ω\text{120.48} \angle 1.95^\circ \Omega.

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