A harmonic AC voltage source with an effective value of 36 V and a frequency of 50 Hz has two identical resistors ( R 1 = R 2 = R ) and a capacitor connected in parallel (figure). Additionally, tw

Question

A harmonic AC voltage source with an effective value of 36 V and a frequency of 50 Hz has two identical resistors $(R_{1} = R_{2} = R)$ and a capacitor connected in parallel (figure). Additionally, two ammeters $A_{1}, A_{2}$ with negligible resistance are included in the circuit. The measured currents are $I_{1} = 5 A, I_{2} = 4 A$ .

TestHub · Accepted Answer

Let each resistor current be r and the capacitor current be c.

A2 reads one resistor plus the capacitor; A1 reads both resistors plus the capacitor.

$r^{2} + c^{2} = I_{2}^{2} = 16$

$(2 r)^{2} + c^{2} = I_{1}^{2} = 25$

$3 r^{2} = 9 \Rightarrow r = 3 A$

$c = 16 - 3 = 13 A$

(A) is false; (B) is true.

$tan φ_{1} = \frac{c}{2 r} = \frac{13}{12}$

(C) is true.

$tan φ_{2} = \frac{c}{r} = \frac{13}{3}$

(D) is false. Answer: B, C.

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