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EE 103 Homework 3 REVIEW PROBLEMS IN PARALLEL
AC CIRCUITS
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, REVIEW PROBLEMS IN PARALLEL AC CIRCUITS
1. A capacitor of 50 μF capacitance is connected in parallel with a reactor of 22 Ω resistance and 0.07
henry inductance across 200-V, 50 Hz mains. Calculate the total current taken. Draw the vector
diagram.
[4.76 A lagging, 17°12’]
2. A non-inductive resistor is connected in series with a capacitor of 100 μF capacitance across a 200-V,
50 Hz mains. The p.d. measured across the resistor is 150 V. Find the value of resistance and the
value of current taken from the mains if the resistor were connected in parallel instead of in series.
[R = 36.1 Ω; 8.37 A]
3. An impedance of (10 + j15) Ω is connected in parallel with an impedance of (6 + j8) Ω. The total
current is 15 A. Calculate the real power.
[2036 W]
4. The load on a 250-V supply system is: 12 A at 0.8 power factor lagging; 10 A at 0.5 power factor
lagging; 15 A at unity power factor; 20 A at 0.6 lagging power factor. Find (a) the load in kVA and (b)
its power factor.
[(a) 10.4 kVA (b) 1.0]
5. A voltage, having a frequency of 50 Hz and expressed by V = 200 + j100 is applied to a circuit
consisting of an impedance of Ω in parallel with a capacitance of 10 μF. Find (a) the
5030
reading on an ammeter connected in the supply circuit (b) the phase difference between the current
and the voltage.
[(a) 4.52 (b) 26.6° lag]
6. A voltage of V is applied in two circuits A and B connected in parallel. The current in A is
20030
and that in B is A. Find the kVA and kW in each branch circuit and the main
2060 40 30
circuit. Express the current in the main circuit in the form a + jb.
[kVAA = 4, kVAB = 8, kVA = 12, kWA = 3.46, kWB = 4, kW = 7.46, I = 44.64 + j2.68]
7. A coil having an impedance of (8 + j6) Ω is connected across a 200-V supply. Express the current in
the coil in (a) polar and (b) rectangular coordinate form.
If a capacitor having a susceptance of 0.1 S is placed in parallel with the coil, find (c) the
magnitude of the current taken from the supply.
[(a) A (b) 16 – j12 A (c) 17.9 A]
20Ð36.8°
8. A coil A of inductance 80 mH and resistance 120 Ω is connected to a 230-V, 50-Hz single phase
supply. In parallel with it is a 16 μF capacitor in series with a 40 Ω non-inductive resistor B.
Determine (a) the power factor of the combined circuit and (b) the total power taken from the supply.
[(a) 0.945 lead (b) 473 W]
9. A choking coil of inductance 0.08 H and resistance 12 ohm is connected in parallel with a capacitor
of 120 μF. The combination is connected to a supply at 240 V, 50 Hz. Determine the total current
from the supply and its power factor.
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Scholarfriends
EE 103 Homework 3 REVIEW PROBLEMS IN PARALLEL
AC CIRCUITS
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in-parallel-ac-circuits
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, REVIEW PROBLEMS IN PARALLEL AC CIRCUITS
1. A capacitor of 50 μF capacitance is connected in parallel with a reactor of 22 Ω resistance and 0.07
henry inductance across 200-V, 50 Hz mains. Calculate the total current taken. Draw the vector
diagram.
[4.76 A lagging, 17°12’]
2. A non-inductive resistor is connected in series with a capacitor of 100 μF capacitance across a 200-V,
50 Hz mains. The p.d. measured across the resistor is 150 V. Find the value of resistance and the
value of current taken from the mains if the resistor were connected in parallel instead of in series.
[R = 36.1 Ω; 8.37 A]
3. An impedance of (10 + j15) Ω is connected in parallel with an impedance of (6 + j8) Ω. The total
current is 15 A. Calculate the real power.
[2036 W]
4. The load on a 250-V supply system is: 12 A at 0.8 power factor lagging; 10 A at 0.5 power factor
lagging; 15 A at unity power factor; 20 A at 0.6 lagging power factor. Find (a) the load in kVA and (b)
its power factor.
[(a) 10.4 kVA (b) 1.0]
5. A voltage, having a frequency of 50 Hz and expressed by V = 200 + j100 is applied to a circuit
consisting of an impedance of Ω in parallel with a capacitance of 10 μF. Find (a) the
5030
reading on an ammeter connected in the supply circuit (b) the phase difference between the current
and the voltage.
[(a) 4.52 (b) 26.6° lag]
6. A voltage of V is applied in two circuits A and B connected in parallel. The current in A is
20030
and that in B is A. Find the kVA and kW in each branch circuit and the main
2060 40 30
circuit. Express the current in the main circuit in the form a + jb.
[kVAA = 4, kVAB = 8, kVA = 12, kWA = 3.46, kWB = 4, kW = 7.46, I = 44.64 + j2.68]
7. A coil having an impedance of (8 + j6) Ω is connected across a 200-V supply. Express the current in
the coil in (a) polar and (b) rectangular coordinate form.
If a capacitor having a susceptance of 0.1 S is placed in parallel with the coil, find (c) the
magnitude of the current taken from the supply.
[(a) A (b) 16 – j12 A (c) 17.9 A]
20Ð36.8°
8. A coil A of inductance 80 mH and resistance 120 Ω is connected to a 230-V, 50-Hz single phase
supply. In parallel with it is a 16 μF capacitor in series with a 40 Ω non-inductive resistor B.
Determine (a) the power factor of the combined circuit and (b) the total power taken from the supply.
[(a) 0.945 lead (b) 473 W]
9. A choking coil of inductance 0.08 H and resistance 12 ohm is connected in parallel with a capacitor
of 120 μF. The combination is connected to a supply at 240 V, 50 Hz. Determine the total current
from the supply and its power factor.
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