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# Module 10.1

# Ideal Parallel Circuits

**After studying this section, you should be able to:**- • Recognise ideal LCR parallel circuits.
- • Describe the effects of internal resistance.

### Fig. 10.1.1 The "Ideal" LC Parallel Circuit

The circuit in Fig 10.1.1 is an "Ideal" LC circuit consisting of only an inductor L and a capacitor C connected in parallel. Ideal circuits exist in theory only of course, but their use makes understanding of basic concepts (hopefully) easier. It allows consideration of the effects of L and C, ignoring any circuit resistance that would be present in a practical circuit.

Fig 10.1.2 shows phasor diagrams for the circuit in Fig 10.1.1 under three different conditions, below, above and at resonance. Unlike the phasor diagrams for series circuits, these diagrams have a voltage V_{S} as the reference (horizontal) phasor, and have several phasors depicting currents. This is because, in a parallel circuit the voltage V_{S} is common to both the L and C arms of the circuit but each of the component arms (L and C) can have individual CURRENTS.

The phasors for L and C seem to be reversed compared with the phasor diagrams for series circuits in module 9, but the parallel phasor diagram shows the current I_{C} through the capacitor leading the supply voltage V_{S} by 90°, while the inductive current I_{L} lags the supply voltage by 90°. (The mnemonic CIVIL introduced in Module 5.1 still works for these diagrams.)

### Fig. 10.1.2 Phasor diagrams for the Ideal LC Parallel Circuit

The supply current I_{S} will be the phasor sum of I_{C} and I_{L} but as, in the ideal circuit, there is no resistance present, I_{C} and I_{L} are exactly in antiphase, and I_{S} will be simply the difference between them.

Fig 10.1.2a shows the circuit operating at some frequency below resonance ƒ_{r} where I_{L} is greater than I_{C} and the total current through the circuit I_{S} is given by I_{L} − I_{C} and will be in phase with I_{L}, and it will be lagging the supply voltage by 90°. Therefore at frequencies below ƒ_{r} more current flows through L than through C and so the parallel circuit acts as an INDUCTOR.

Fig 10.1.2b shows the conditions when the circuit is operating above ƒ_{r}.
Here, because X_{C} will be lower than X_{L} more current will flow through C. I_{C} is therefore greater than I_{L} and as a result, the total circuit current I_{S} can be given as I_{L} − I_{C} but this time I_{S} is in phase with I_{C}. The circuit is now acting as a CAPACITOR.

Notice that in both of the above cases the parallel circuit seems to act in the opposite manner to the series circuit described in AC Theory Module 9.1. The series circuit behaved like a capacitor below resonance and an inductor above. The parallel circuit is acting like an inductor below resonance and a capacitor above. This change is because the parallel circuit action is considered in terms of current through the reactances, instead of voltage across the reactances as in the series circuit.

At resonance (ƒ_{r}) shown in Fig 10.1.2c, the reactances of C and L will be equal, so an equal amount of current flows in each arm of the circuit, (I_{C} = I_{L}). This produces a very strange condition. Considerable current is flowing in each arm of the circuit, but the supply current is ZERO! There is no phasor for I_{S}! This impossible state of affairs of having currents flowing around the circuit with no supply current, indicates that the circuit must have infinite impedance to the supply. As there is no resistance in either L or C in the ideal circuit, current continues to flow from L to C and back again. This only happens of course in an ideal circuit, due to the complete absence of resistance in either arm of the circuit, but it is surprisingly close to what actually happens in a practical circuit, because current is in effect "stored" within the parallel circuit at resonance, without being released to the outside world. For this reason the circuit is sometimes also called a "tank circuit".