In The Figure What Value Must R Have

Reading a Resistor's Value Straight Off the Figure

Most circuit diagrams hand you a resistor's value right on the page. In practice, other times, you get a letter code, a band pattern, or a symbol that needs a quick lookup. Sometimes it's printed as a number — 220, 1k, 47k — and you're done. And then there are the diagrams that show a variable resistor with a single value next to it, almost like the author is daring you to figure out what range it covers.

The question "what value must r have" usually shows up in two different contexts, and they need different answers. That said, the other is practical — you're looking at a component in a real circuit and trying to read its value from the figure itself. Practically speaking, one is theoretical — you're staring at a circuit drawn on paper, and r is a specific resistor whose value is needed to make some condition true (maximum power transfer, balance in a bridge, a particular output voltage). Let's work through both, because the trick is knowing which one you're actually being asked.

What "r" Usually Refers To in a Circuit

In almost every textbook figure, r is the symbol for resistance, expressed in ohms. It can mean a fixed resistor, the internal resistance of a source, or the value of a variable resistor set to some particular position. The lowercase r often refers to a small or internal resistance, while a capital R tends to mean an external or load resistor — but conventions vary, so check the figure's own legend if one is provided.

The value of r depends entirely on the question attached to the figure. If the diagram shows a Thévenin equivalent circuit and asks for the load that draws maximum power, r will be a specific ohms figure that equals the source's internal resistance. Even so, if the figure shows a Wheatstone bridge and asks when it's balanced, r is the unknown you're solving for algebraically. The figure itself doesn't give* you r in those cases — it gives you the conditions, and you do the math.

When the Figure Actually Shows the Value

Some figures are more direct. A resistor symbol with "r = 220 Ω" written beside it is telling you the value outright. Same with "r = 1.2 kΩ" or "r = 4.7 MΩ." If you see a number, that's your answer. But diagrams sometimes use shorthand that catches beginners off guard.

Reading Letter and Number Codes

European and Japanese schematics often mark resistors with codes like 4R7, 2K2, or 1M5. 2 kilohms, and 1M5 means 1.Because of that, the letter acts as a decimal point, and the suffix tells you the multiplier. So 4R7 means 4.Here's the thing — 5 megohms. On the flip side, 7 ohms, 2K2 means 2. Once you know the trick, these are actually easier to read than hunting for a decimal point in a string of digits.

A "k" by itself after a number means thousands, and "M" means millions. Some figures drop the unit entirely, so 470 next to a resistor is assumed to be ohms unless something else is indicated. 2 megohms. So 470k = 470,000 Ω, and 2M2 = 2.That's a convention worth checking before you commit to a value.

Reading Color Bands on a Resistor

If the figure is a photograph of a real resistor instead of a schematic symbol, you're looking at color bands. Even so, a five-band resistor adds a third significant digit. So a four-band resistor gives you two significant digits, a multiplier, and a tolerance. Six-band resistors exist too, mostly for high-precision applications, with the extra band indicating temperature coefficient.

Here's the band order you need to memorize:

Digit colors: black = 0, brown = 1, red = 2, orange = 3, yellow = 4, green = 5, blue = 6, violet = 7, gray = 8, white = 9
Multiplier colors: same colors, but the value is the power of ten — so red = ×100, yellow = ×10,000
Tolerance: gold = ±5%, silver = ±10%, brown = ±1%, red = ±2%
Temperature coefficient (sixth band): brown = 100 ppm, red = 50 ppm, orange = 15 ppm, yellow = 25 ppm

A real example: yellow-violet-red-gold reads 4-7-×100-±5%, which is 4,700 Ω (or 4.Now, 7 kΩ) with 5% tolerance. Worth knowing: blue body color used to mean a non-flammable resistor, but that convention has faded out, so don't rely on it.

When You Have to Solve for r

The harder case is the textbook problem where the figure shows a network and asks what r must equal. The figure gives you the topology, and the question gives you the constraint. Here are the most common scenarios.

Maximum Power Transfer

If the figure shows a source with internal resistance driving a load r, and the question asks when the load gets maximum power, the answer is r = R_internal. So the load resistance should match the Thévenin resistance seen from its terminals. Any higher or lower, and the power drops off.

Bridge Balance

A Wheatstone bridge figure with a galvanometer in the middle and a question about r typically wants r set so the bridge balances — meaning no current flows through the detector. The condition is that the ratios of the four arms are equal: R1/R2 = R3/R4, or however the figure labels them. Solve for r using the three known values.

Output Voltage or Current Targets

Sometimes the figure shows a voltage divider or current divider, and the question is what r must be to produce a specific output. Consider this: this is a straightforward algebra problem once you write down the divider equation. A voltage divider gives you Vout = Vin × r2/(r1+r2), and you rearrange to solve for whichever resistor is unknown.

Common Mistakes When Reading r From a Figure

The first mistake is assuming the unit shown is ohms. Some schematics label resistors in kilohms or megohms without making it obvious. Now, if a resistor is marked "470" and the rest of the circuit is in kilohms, you've just read a value 1,000 times too small. Always look for a unit or a multiplier letter before trusting the number.

For more on this topic, read our article on how many minutes are in 6 hours or check out two lines are intersecting what is the value of x.

The second mistake is confusing r and R. Lowercase r often means internal or parasitic resistance in a source, while uppercase R means an external component. If the figure asks "what value must r have" and the symbol in the diagram is capitalized, the question is using lowercase loosely — but check the actual symbol on the page, not the question's typography.

The third mistake is reading color bands under bad lighting or with color-blindness issues. Red and brown bands are notoriously easy to mix up, as are orange and yellow. If the band order is critical, hold the resistor under a bright white light and compare against a known reference. Many online calculators let you input band colors directly, which removes the guesswork.

The fourth mistake is ignoring tolerance. A resistor marked 1 kΩ with ±5% tolerance can be anywhere from 950 Ω to 1,050 Ω. If the circuit only works in a narrow range, the nominal value isn't enough — you need to know the actual measured resistance with a multimeter.

Practical Tips for Getting r Right

If you're working from a schematic, sketch out the circuit yourself before trusting any label. Still, redrawing forces you to read every component and confirm the values match what's written. It also catches the case where the figure has a typo or uses inconsistent notation.

If you're working from a photograph or a real component, use a multimeter whenever possible. Color codes are a fallback, not a primary method. A five-second resistance check beats ten seconds of squinting at bands, every time.

If the question is theoretical and you're stuck, write the loop equations for the circuit and solve them. Most "what must r equal" questions reduce to a single algebraic equation once you apply Kirchhoff's voltage law around the right loop. The figure is just there to give you the topology — the math is yours to do.

And finally, if a figure shows a variable resistor (a resistor symbol with an arrow through it), remember that r is whatever position the wiper is set to. The figure will usually either give you that position or ask you to find it. A potentiometer at "50% rotation" gives you half its total resistance, not a fixed value.

Don't assume the labeled value without confirming the actual setting. In a schematic, a variable resistor is often shown with an arrow that pierces the resistor body, indicating the wiper's position. If the diagram does not specify that position, you must either infer it from the context of the problem or treat the component as an unknown that you will solve for. A potentiometer rated at 10 kΩ, for example, will present any resistance between 0 Ω and 10 kΩ depending on the rotation; assuming it is fixed at its nominal value will almost certainly lead to an incorrect answer.

Putting It All Together

When you approach a circuit problem that involves a resistance labeled r (or R), keep the following checklist in mind:

Unit clarity – Verify that the schematic’s units match the problem statement. A “470” in a kilohm‑scaled circuit is 470 kΩ, not 470 Ω.
Symbolic distinction – Distinguish between lowercase r (often internal or parasitic) and uppercase R (an external component). Check the actual diagram, not just the wording of the question.
Color‑band confidence – If you must read a resistor’s value from its bands, do so under bright, neutral lighting. Use a reference chart or an online calculator to eliminate ambiguity between similar colors such as red/brown or orange/yellow.
Tolerance awareness – Know the tolerance of the component. A ±5 % resistor can swing a full 10 % from its nominal value, which may be decisive in tight‑tolerance designs.
Instrument verification – Whenever possible, measure the actual resistance with a multimeter. It is faster and far more reliable than decoding bands or trusting printed labels.
Redraw the schematic – Sketching the circuit yourself forces you to read every component and catches typographical errors or inconsistent notation that a quick glance might miss.
Apply the fundamentals – Write Kirchhoff’s voltage or current equations for the loop that contains r. Most “what must r be?” problems reduce to a single algebraic expression once the correct loop is identified.
Variable resistors – Treat a potentiometer or variable resistor as a dynamic element. Its resistance depends on the wiper’s position, which must be either given in the problem or solved for using the circuit equations.

Final Thoughts

Mastering the interpretation of resistance symbols—whether they are fixed values, tolerances, or variable settings—turns a seemingly minor detail into a powerful tool for circuit analysis. The mistakes highlighted here are common, but they are also avoidable with a disciplined approach: confirm units, verify symbols, use a multimeter when in doubt, and always double‑check the physical or schematic representation against the mathematics of the circuit.

By integrating these practices into your routine, you will not only answer “what must r equal?” questions accurately, but you will also develop a deeper intuition for how resistors behave in real‑world designs. In the end, the confidence to trust your own analysis—and to spot the subtle pitfalls that others overlook—is what separates a competent engineer from a truly skilled one.