The core idea
Charge is conserved as it circulates through a steady circuit, while energy moves from a source to components and their surroundings. For an ohmic resistor under unchanged conditions, V = IR; series and parallel arrangements obey different connection rules.
1. Count the charge crossing a section
Electric charge is a property of matter, measured in coulombs, C. Current describes the rate of net charge flow through a chosen cross-section. For steady current, I = Q/t, where Q is the charge that crosses in time t. With seconds and coulombs, current is in amperes: 1 A = 1 C/s. Metallic wires contain mobile electrons; their drift is opposite to the conventional current direction, which follows positive-charge motion. A resistor does not consume the charge passing through it. In a steady, unbranched circuit, the same current passes every section because charge is not continually accumulating at one point. Current is a flow rate, not an amount stored in a wire.
Sources: NCERT: Electricity ↗ · OpenStax: Model of Conduction in Metals ↗
2. Track energy per charge
Potential difference, often called voltage, describes energy transferred per unit charge between two points. Its unit is volt, V, with 1 V = 1 J/C. For a component receiving electrical energy E as charge Q passes, E = VQ when the voltage is constant. A cell uses chemical processes to maintain a potential difference; in a complete circuit, the electric field drives charges already present in the conductors. Opening a switch breaks the conducting path and stops steady current, but a potential difference can remain across the open gap. A voltmeter compares two points, whereas an ammeter measures the flow through a path. These are different measurements, not interchangeable readings of “electricity.”
Sources: NCERT: Electricity ↗ · OpenStax: Model of Conduction in Metals ↗
3. State when Ohm’s law applies
For an ohmic resistor with temperature and other physical conditions unchanged, current is proportional to voltage: V = IR. Resistance R is measured in ohms, Ω, where 1 Ω = 1 V/A. At fixed voltage, more resistance means less current. Microscopic interactions between moving charge carriers and the material transfer energy into random motion and other internal processes. This accounts for resistive heating without consuming charge. Resistance depends on material, dimensions and temperature. A longer uniform wire usually has more resistance, while a larger cross-sectional area offers more conducting paths. Not every component obeys a straight-line voltage-current relation; the constant-R model must be justified rather than applied automatically.
Sources: NCERT: Electricity ↗ · OpenStax: Model of Conduction in Metals ↗
4. Read connections before calculating
In series, components share one unbranched path, so they carry the same steady current. Their voltage drops add to the source voltage in an ideal loop, and Rtotal = R₁ + R₂. In parallel, branches connect across the same two nodes, so they share a voltage; branch currents add at the junction. For two resistors, 1/Rtotal = 1/R₁ + 1/R₂. A node means electrically connected points joined by ideal wires. Parallel does not merely mean that two symbols look side by side on paper. Follow the connections. In theoretical meter diagrams, an ammeter belongs in the measured path and a voltmeter across the two compared points.
Sources: NCERT: Electricity ↗
5. Keep energy and charge accounts separate
Combining E = VQ with Q = It gives E = VIt for constant voltage and current. Dividing by time gives electrical power P = VI in watts, W; one watt is one joule per second. For an ohmic resistor, substituting V = IR gives P = I²R and E = I²Rt. An ideal resistor transfers electrical energy into internal energy, eventually heating its surroundings. A lamp may also produce light and a motor mechanical output. The source must supply these energy transfers even though charge returns around the circuit. All examples here are paper models with ideal sources and negligible wire resistance; they are not circuit-building instructions.
Sources: NCERT: Electricity ↗
6. Worked example: sharing a voltage in series
Illustrative circuit: an ideal 6 V source supplies 4 Ω and 8 Ω resistors in series. Total resistance is 12 Ω, so current I = 6/12 = 0.50 A throughout. The first voltage drop is 0.50 × 4 = 2 V and the second is 0.50 × 8 = 4 V; together they match 6 V. Source power is 6 × 0.50 = 3 W. Over 60 s, the source supplies 180 J. The resistors receive 60 J and 120 J respectively, adding to 180 J. The second resistor receives more energy per coulomb, but both carry the same charge per second.
One series path: same current, shared voltage
| Component | Resistance | Current | Voltage drop |
|---|---|---|---|
| First resistor | 4 Ω | 0.50 A | 2 V |
| Second resistor | 8 Ω | 0.50 A | 4 V |
| Series total | 12 Ω | 0.50 A | 6 V |
Sources: NCERT: Electricity ↗
7. Worked example: sharing current at a junction
In a separate hypothetical model, 6 Ω and 3 Ω resistors are in parallel across an ideal 6 V source. Both branches have 6 V. Their currents are 6/6 = 1 A and 6/3 = 2 A. The source current is 3 A, so equivalent resistance is 6/3 = 2 Ω, smaller than either branch resistance. The source power is 6 × 3 = 18 W; branch powers are 6 W and 12 W. Adding a parallel conducting branch can therefore increase source current at fixed voltage. Real cells may have internal resistance and limited output, so this ideal prediction does not describe every battery under heavy load.
Sources: NCERT: Electricity ↗
PUT IT INTO PRACTICE
Apply it and check your reasoning
- Draw a hypothetical ideal 3 V source and a 6 Ω resistor in a closed loop on paper. Predict current and calculate the charge passing in 20 s.
- Calculate power and transferred energy. Then redraw the switch open and distinguish the steady-current prediction from the voltage across the gap.
- Check: I = 0.50 A, Q = 10 C, P = 1.50 W and E = 30 J. With the ideal switch open, steady current is zero; the source can still maintain 3 V across the gap.
Check your understanding
Why is current not smaller after a series resistor?
In steady flow, charge cannot continually collect inside the resistor. The same charge per second enters and leaves, while energy is transferred to the resistor.
Can voltage exist without steady current?
Yes. An open circuit can retain a potential difference even though it lacks a complete conducting path.
Why must temperature be specified for a constant-resistance model?
Material interactions and resistance can change with temperature. A component that heats appreciably may not retain the resistance assumed in the calculation.
Why is equivalent parallel resistance less than either positive branch resistance?
The added branch offers another path, increasing total current at the same voltage. Therefore the ratio of source voltage to total current decreases.
What does a battery supply if it does not supply freshly created charge?
Chemical processes transfer energy and maintain a potential difference that drives existing charges. The energy budget changes while total charge remains conserved.