Source: https://mokxi.com/learn/circuit-lab-division-c Learn # Circuit Lab Division C: what high school adds, on circuits you can run Written by the Mokxi team Start building free Or see every lesson. - 500 parts on the bench - 43 boards running now - 1.00x real time, on every board Click to open it in the editor 12 V into 4.7 k, 10 k and 2.2 k on top, and 8.16 V behind 5.40 k below. Both drive a 10 k load, and both meters read about 5.30 V. Division C is the high school side of Science Olympiad Circuit Lab, and Circuit Lab is on the 2027 event list for both Division B and Division C. The ideas start where a middle school team starts, with Ohm’s law, series and parallel and a meter, and then go further: two sources at once, equivalent circuits, circuits that change in time, AC, and parts that are not resistors. Each topic below ends in a circuit you open in the editor, and every number is what the simulator reads on it. Work it on paper first, then press Run and check. Read the current Division C rules at soinc.org before you plan your study. They set the topic list, the notes you may bring and the calculators allowed, and they change from season to season. Confirm the event with your own tournament as well. This guide is not affiliated with Science Olympiad. ## What Division C adds over Division B A Division B question can nearly always be solved with one source and a series or parallel shortcut. Division C questions often go where the shortcut stops working: two sources in one network, a capacitor or inductor that makes the answer depend on time, a sine wave whose voltages no longer simply add, or a diode, transistor or op-amp to work out first. If your team is new to the event, start with the Division B guide and the main study guide, and come back once Ohm’s law is automatic. ## Two sources: Kirchhoff and node analysis Name the unknown node, write the current law there, and solve. In the two-source circuit, 12 V feeds node A through 1 k and 6 V feeds it through 2 k, with 3 k from A to ground. The current law at A is (12 - VA) / 1 k + (6 - VA) / 2 k = VA / 3 k, which gives VA = 8.18 V. The meter reads 8.18 V. Then read the branches. The 1 k carries 3.82 mA into A and the 3 k carries 2.73 mA from A to ground. The other 1.09 mA leaves through the 2 k and flows backward into the 6 V source, because A is higher than 6 V. A negative branch current in your working only means you guessed the direction wrong. ## Thevenin and Norton equivalents Seen from two terminals, any network of sources and resistors is one source behind one resistor. In the circuit at the top, 12 V drives R1 (4.7 k) into a node with R2 (10 k) to ground and R3 (2.2 k) out to the load. Take the load off and R1 and R2 are a divider: Vth = 12 x 10 / 14.7 = 8.16 V. Short the source and look back in: 4.7 k in parallel with 10 k is 3.20 k, and R3 makes Rth = 5.40 k. The bottom half of that circuit is the equivalent, and with 10 k loads both meters read about 5.30 V. The Norton form is the same thing turned around: a current source of Vth / Rth in parallel with Rth. Make both loads 1 ohm, nearly a short, and each carries about 1.51 mA, the Norton current. 8.16 V / 1.51 mA = 5.40 k, so the open-circuit voltage and the short-circuit current give you Rth without taking the network apart. ## RC transients A capacitor charging through a resistor follows V = Vs x (1 - e^(-t / RC)). The time constant is tau = R x C: after one tau it is 63 percent of the way, after five it is all but there. With 10 k and 100 uF, tau is one second. Flip the switch in the RC circuit and the scope reads about 3.14 V at one second and 4.29 V at two, on a 5 V supply. The scope’s 1 megohm input loads the capacitor, so it levels off at about 4.95 V rather than 5.00 V, as on a real bench. ## RL transients An inductor resists a change in current the way a capacitor resists a change in voltage. Its time constant is tau = L / R. The RL circuit has 100 mH in series with 100 ohms, so tau is 1 ms, and the scope reads the resistor, whose voltage is the current times 100 ohms. Flip the switch and one millisecond later the resistor reads about 3.16 V, 63 percent of 5 V, so the current is 31.6 mA of its final 50 mA. At 5 ms it reads about 4.96 V. Flip the switch back and the current dies away the same way: one millisecond later the resistor reads about 1.84 V, 37 percent of where it started. At the instant a switch closes, a capacitor acts like a short and an inductor like an open. Long after, it is the other way around. ## AC: reactance and phasors A capacitor’s opposition to AC is its reactance, Xc = 1 / (2 pi f C), and an inductor’s is XL = 2 pi f L. The AC circuit drives 1 k and 1 uF in series from a 60 Hz sine of 10 V peak, which is 7.07 V RMS. At 60 Hz the capacitor is about 2.65 k. The AC meters read about 2.50 mA, 2.50 V across the resistor and 6.60 V across the capacitor, and 6.60 V / 2.50 mA is 2.64 k: the reactance, measured. Those two voltages add up to 9.10 V, more than the 7.07 V going in. They add as phasors, at right angles, because the capacitor’s voltage lags the current by 90 degrees: the square root of 2.50 squared plus 6.60 squared is 7.06 V. The impedance adds the same way: about 2.83 k. ## Resonance In series, an inductor’s and a capacitor’s reactances cancel at one frequency, f0 = 1 / (2 pi x root(L x C)). The RLC circuit has 250 ohms, 10 mH and 2.5 nF, so f0 is about 31.8 kHz and Q = (1 / R) x root(L / C) = 8.0. Sweep it from the Analysis menu and the voltage across the capacitor peaks at about 17.9 dB, about 7.9 times the input, near 31.6 kHz. That peak sits a little under f0, because the capacitor’s voltage peaks slightly below resonance; the current peaks right on it. ## Diodes A conducting silicon diode drops roughly 0.7 V, and an LED more. The diode circuit puts 330 ohms from 5 V into a 1N4148 and into a red LED. The meter reads 0.74 V across the diode, and the LED drops about 1.65 V and passes about 10.2 mA, which is (5 - 1.65) / 330. ## Transistors An NPN transistor used as a switch is either off or saturated. In the transistor circuit a 2N2222 switches a red LED and 470 ohms from 9 V, with a 10 k base resistor. With the base on ground the meter reads 7.96 V from collector to emitter. Switch the base to 9 V and it reads 0.06 V: saturated. The base current is about (9 - 0.73) / 10 k = 0.83 mA and the collector current about 15.3 mA, only about 19 times as much. That is well under a 2N2222’s datasheet gain: the base has more current than the load needs, which is what saturated means. ## Op-amps An ideal op-amp with negative feedback drives its output until its two inputs are equal. In the op-amp circuit a 10 k over 2.2 k divider puts 1.62 V on IN+, and the 22 k and 10 k feedback set a gain of 1 + 22 / 10 = 3.2, so the output should be 1.62 x 3.2 = 5.19 V. The meter reads 5.19 V, and IN- sits at 1.62 V, the same as IN+. Change the 22 k to 47 k and the gain of 5.7 asks for about 9.25 V, more than the 9 V supply. The output stops at about 8.98 V, against the rail. A real op-amp would stop somewhat lower. ## Meter loading A voltmeter is a large resistor across whatever it measures: 10 megohms here, as on most digital meters. Across the bottom of two 10 megohm resistors on 10 V, that makes 5 megohms against 10, and the meter reads 3.33 V instead of 5.00 V. With 10 k resistors the same meter reads 5.00 V. An ammeter loads a circuit too. This one is a 1 ohm shunt, which is why the Ohm’s law circuit, 9 V across 470 ohms, reads 19.11 mA where 9 / 470 gives 19.15 mA. ## What Mokxi does not cover Mokxi simulates circuits. It does not model magnetism: magnetic fields, the force on a current-carrying wire, and induction as physics are not here, beyond an inductor in a circuit. It does not cover the history of electricity or the people the units are named after, which past Division C rules have included. Check this season’s rules for whether they are on the list. It is also not a real bench: the hands-on tasks are done on real equipment, so practice on a real meter too. The cheat sheet has the formulas on one page, and the practice test is a timed run. ## Questions Is Circuit Lab a Division C event in 2027? Circuit Lab is on Science Olympiad’s 2027 event list for Division C, and for Division B. Check soinc.org and your own tournament, which may schedule events differently. What is the difference between Circuit Lab Division B and Division C? Division C is written for high school, so the questions go past one source and a series or parallel shortcut: two-source networks, equivalent circuits, transients, AC and semiconductors. The current rules at soinc.org give the exact topic list for each division. Related ## Keep going Science Olympiad Circuit Lab Study Guide, B and C Circuit Lab Practice Test: 30 Measured Questions Circuit Lab Cheat Sheet: Formulas With Examples Circuit Lab Division B: Middle School Starter Guide RLC Circuit Simulator: Series Resonance and Q, Live The RC Time Constant, on an Oscilloscope The Thevenin simulator The AC circuit simulator The op-amp simulator ## Build this for real Open the editor, change a value and watch the number move with it. Nothing to install, and no account needed. Start building free Open the editor