RLC parallel circuits

IR = ET / R (in phase with ET) IL = ET / XL (lags ET by 90°) IC = ET / XC (leads ET by 90°)

Net reactive current = |IL − IC|

IT = √[IR² + (IL − IC)²]

Z = ET / IT

When IL and IC nearly cancel, IT approaches IR and Z rises toward R — heading into parallel resonance territory (next lesson).

Same definitions: watts in R, VARs in L and C, VA from ET×IT. Net VARs = |VARsL − VARsC|.

Motors (inductive), lighting/resistive loads, and PF capacitors often share a bus — a parallel mix. You rarely have a textbook three-branch lab circuit, but the current-cancellation idea is exactly how PF capacitors reduce line current for the same mechanical work.

1. Find XL and XC at the operating frequency.
2. Compute each branch current.
3. Subtract reactive currents.
4. Combine with IR for IT.
5. Find Z, PF = IR/IT, θ.

Contrast with series RLC: there you subtracted reactances (ohms); here you subtract reactive currents (amps).

ET=120 V, R=30 Ω, XL=40 Ω, XC=60 Ω:

IR=4 A, IL=3 A, IC=2 A Net reactive = 1 A lagging IT=√(16+1)=4.12 A PF=4/4.12≈0.97 lagging

If you raise C until XC=40 Ω, IC=3 A, net reactive=0, IT=IR=4 A — parallel resonance neighborhood for the LC pair with R still taking current.

A motor is roughly R-L. Adding C in parallel is this lesson. Feeder current can fall while motor shaft load stays the same because VARs cancel.

Clamp the feeder and the capacitor branch separately. The difference story teaches cancellation better than any paragraph.

Situation. A motor draws 40 A. After PF capacitors are paralleled at the motor, the feeder clamp reads 28 A while the motor still does the same work.

What happened. Capacitive current canceled much of the motor’s lagging reactive current. Real power is similar; line VA dropped.

Applied lesson. Parallel reactive cancellation lowers IT without “creating energy.” Verify motor amps separately from feeder amps when caps are local.

### Teaching pause — say this out loud

Before you leave this lesson, explain the main idea to an imaginary first-month helper in under one minute. If you need the book open to do it, reread How it works once more. Field diagnosis only helps after the concept is yours.

Also sketch the key diagram from memory (triangle, wye/delta, filter shape, or charge curve — whichever this lesson used). Labels beat artistic skill.

### Why this lesson matters on Monday morning

RLC parallel circuits is not trivia. You will meet it when a meter reading looks “impossible,” when a replacement part is almost right, or when a helper asks why the book uses √3 or lead/lag. Master the model here so the next call is pattern recognition, not panic.

Common Monday uses: verify a nameplate against clamps, explain a PF or capacitor change to a customer, or catch a miswired series/parallel or wye/delta assumption before energizing.