What Is Ohm's Law?
Ohm's Law is one of the most fundamental relationships in physics and electrical engineering. Discovered by German physicist Georg Ohm in 1827, it states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, with the constant of proportionality being the resistance (R). The formula is V = IR.
In plain language: voltage is the electrical pressure that pushes current through a circuit, current is the flow of electric charge (measured in amperes), and resistance is how much the conductor opposes that flow (measured in ohms). Increase the voltage and the current increases. Increase the resistance and the current decreases. That is the essence of Ohm's Law.
The water analogy helps many students understand these concepts. Think of voltage as water pressure in a pipe, current as the flow rate of water, and resistance as the width of the pipe. Higher pressure (voltage) pushes more water (current) through. A narrower pipe (higher resistance) restricts the flow. This analogy is imperfect but captures the key relationships.
The Three Forms of the Formula
Ohm's Law can be rearranged into three forms depending on which variable you need to find. V = IR (find voltage when you know current and resistance). I = V/R (find current when you know voltage and resistance). R = V/I (find resistance when you know voltage and current).
A useful memory aid is the Ohm's Law triangle. Draw a triangle and divide it into three sections: V on top, I on the bottom-left, R on the bottom-right. To find any variable, cover it with your finger — the remaining two variables show the formula. Cover V: you see I x R (V = IR). Cover I: you see V over R (I = V/R). Cover R: you see V over I (R = V/I).
Units matter. Voltage is measured in volts (V), current in amperes or amps (A), and resistance in ohms (the Greek letter omega). The formula works correctly only when all values are in these standard SI units. If resistance is given in kilohms (1 kilohm = 1,000 ohms), convert to ohms first. If current is in milliamps (1 mA = 0.001 A), convert to amps first.
Worked Examples: Applying V = IR
Example 1 (Find Voltage): A 5-amp current flows through a 12-ohm resistor. What is the voltage? V = IR = 5 A x 12 ohms = 60 V. The voltage across the resistor is 60 volts.
Example 2 (Find Current): A 9-volt battery is connected to a 3-ohm resistor. How much current flows? I = V/R = 9 V / 3 ohms = 3 A. Three amperes of current flow through the circuit.
Example 3 (Find Resistance): A 120-volt outlet provides 0.5 amps of current to a device. What is the device's resistance? R = V/I = 120 V / 0.5 A = 240 ohms. The device has 240 ohms of resistance.
Example 4 (Unit Conversion): A circuit has 5 kilohms of resistance and a current of 2 milliamps. Find the voltage. Convert: R = 5,000 ohms, I = 0.002 A. V = IR = 0.002 x 5,000 = 10 V. Always convert to base SI units before plugging into the formula.
Ohm's Law in Series Circuits
In a series circuit, all components are connected end-to-end in a single path. The same current flows through every component, but the voltage divides among them. The total resistance is the sum of all individual resistances: R_total = R1 + R2 + R3 + ...
Example: Three resistors (4 ohms, 6 ohms, and 10 ohms) are connected in series to a 40-volt battery. R_total = 4 + 6 + 10 = 20 ohms. Total current: I = V/R = 40/20 = 2 A. This same 2 A flows through each resistor.
The voltage across each resistor (called the voltage drop) is found using V = IR for each one: V1 = 2 x 4 = 8 V. V2 = 2 x 6 = 12 V. V3 = 2 x 10 = 20 V. Check: 8 + 12 + 20 = 40 V, which equals the battery voltage. In a series circuit, the voltage drops always sum to the source voltage — this is Kirchhoff's Voltage Law.
A practical application: if one component in a series circuit fails (breaks the connection), the entire circuit stops working because there is only one path for current. This is why old-style Christmas lights would all go out when one bulb burned out — they were connected in series.
Ohm's Law in Parallel Circuits
In a parallel circuit, components are connected across the same two points, providing multiple paths for current. The voltage across each branch is the same (equal to the source voltage), but the current divides among the branches. The total resistance follows the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
Example: Two resistors (6 ohms and 3 ohms) are connected in parallel to a 12-volt battery. 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. R_total = 2 ohms. Notice that the total resistance (2 ohms) is less than the smallest individual resistor (3 ohms). This is always true in parallel circuits — adding more paths reduces total resistance.
Current through each branch: I1 = V/R1 = 12/6 = 2 A. I2 = V/R2 = 12/3 = 4 A. Total current: I_total = 2 + 4 = 6 A. Check with Ohm's Law: I_total = V/R_total = 12/2 = 6 A. In a parallel circuit, the branch currents always sum to the total current — this is Kirchhoff's Current Law.
Most household wiring uses parallel circuits. Each outlet receives the same voltage (120 V in the US), and each device draws current independently. If one device is unplugged or fails, the others continue working because each has its own path to the power source.
Electric Power and Ohm's Law
Electric power (P), measured in watts (W), is the rate at which electrical energy is consumed or produced. The basic power formula is P = IV (power equals current times voltage). By substituting Ohm's Law, you can derive two more power formulas: P = I^2R (substitute V = IR into P = IV) and P = V^2/R (substitute I = V/R into P = IV).
These three power formulas let you calculate power from any two known quantities. If you know current and resistance, use P = I^2R. If you know voltage and resistance, use P = V^2/R. If you know voltage and current, use P = IV.
Example: A 100-watt light bulb is connected to a 120-volt outlet. What is the current? P = IV, so I = P/V = 100/120 = 0.833 A. What is the resistance? R = V/I = 120/0.833 = 144 ohms. Or directly: R = V^2/P = 14400/100 = 144 ohms.
Understanding power is important for practical electrical safety. A circuit breaker trips when the current exceeds a safe threshold (typically 15 or 20 amps for household circuits). If you plug too many high-wattage devices into the same circuit, the total current exceeds the breaker's rating and it trips to prevent overheating and fire.
Common Mistakes with Ohm's Law
The most common mistake is using inconsistent units. If resistance is in kilohms and you use it directly in V = IR with current in amps, your voltage will be off by a factor of 1000. Always convert to base units (volts, amps, ohms) before calculating.
Confusing series and parallel formulas is another frequent error. Resistances add directly in series (R_total = R1 + R2) but use the reciprocal formula in parallel (1/R_total = 1/R1 + 1/R2). Using the wrong formula gives the wrong total resistance, which cascades into wrong values for current and voltage.
Students sometimes apply Ohm's Law to an entire circuit when they should apply it to individual components, or vice versa. In a series circuit, the total voltage equals V = I x R_total, but the voltage across one resistor is V_n = I x R_n. In a parallel circuit, the current through one branch is I_n = V / R_n, but the total current is I_total = V / R_total.
Finally, remember that Ohm's Law applies to ohmic resistors — components where the resistance is constant regardless of voltage and current. Some devices (like light bulbs and diodes) have resistance that changes with temperature or applied voltage. For these nonlinear components, Ohm's Law gives approximate results. For help with circuit analysis problems, snap a photo and send it to ScanSolve for a step-by-step solution.
Practice Problems
Problem 1: A 24-volt battery is connected to a 8-ohm resistor. Find the current and power dissipated. Solution: I = V/R = 24/8 = 3 A. P = IV = 3 x 24 = 72 W (or P = V^2/R = 576/8 = 72 W).
Problem 2: Three resistors of 10, 20, and 30 ohms are connected in series to a 60-volt source. Find the total current and the voltage across each resistor. Solution: R_total = 60 ohms. I = 60/60 = 1 A. V1 = 10 V, V2 = 20 V, V3 = 30 V.
Problem 3: Two resistors of 12 ohms and 4 ohms are connected in parallel. The source voltage is 24 V. Find the total resistance, total current, and current through each resistor. Solution: 1/R_total = 1/12 + 1/4 = 1/12 + 3/12 = 4/12. R_total = 3 ohms. I_total = 24/3 = 8 A. I1 = 24/12 = 2 A. I2 = 24/4 = 6 A. Check: 2 + 6 = 8 A.
Problem 4: A device draws 2.5 A from a 230 V outlet. What is the device's resistance and power consumption? Solution: R = V/I = 230/2.5 = 92 ohms. P = IV = 2.5 x 230 = 575 W.