MHT CET Current Electricity: Formulas, Examples and Common Mistakes

For Current Electricity, identify the circuit connections and what the source holds constant before choosing a formula. Use Ohm's law for an ohmic resistor, reduce series or parallel combinations where valid, and distinguish terminal voltage from a cell's emf when internal resistance matters.

The examples below are original teaching examples, not claimed previous-year MHT CET questions. Use them alongside your textbook and the Current Electricity chapter page.

Which formulas should I understand first?

For an ohmic resistor, V = IR. Resistance of a uniform conductor is R = ρL/A, where ρ is resistivity, L is length and A is cross-sectional area. Resistivity depends on material and temperature.

For resistors in series, R_total = R1 + R2 + ... . For parallel resistors, 1/R_total = 1/R1 + 1/R2 + ... .

Electrical power is P = VI. For an ohmic resistor, substitution gives P = I²R and P = V²/R. Energy transferred at constant power is E = Pt.

Write units beside the symbols: volts, amperes, ohms, watts and seconds. In R = ρL/A, using centimetres for length and square millimetres for area without conversion can produce a large numerical error.

How do I tell series from parallel?

Two elements are in series when their common junction has no additional current branch, so the same current flows through them. They are in parallel when both connect across the same two nodes, so they have the same potential difference.

Do not classify a connection from how the drawing looks. Redraw the nodes when wires bend or cross. A wire crossing is not necessarily a junction unless the circuit specifies a connection.

Example: Two resistors, 3 Ω and 6 Ω, are connected in parallel across an ideal 12 V source. Their equivalent resistance is (3 × 6)/(3 + 6) = 2 Ω. Total current is 12/2 = 6 A. Branch currents are 4 A and 2 A, which add to the total.

The equivalent resistance is smaller than either branch resistance. That is a useful check for positive resistances in parallel.

How does the same pair behave in series?

Connect the same 3 Ω and 6 Ω resistors in series across an ideal 12 V source. The equivalent resistance is 9 Ω, so current is 12/9 = 4/3 A.

Voltage drops are 4 V across the 3 Ω resistor and 8 V across the 6 Ω resistor. They add to the source voltage.

Compare the two examples: parallel branches share voltage; series elements share current. The resistor values have not changed, but their connection changes the total current. This is why identifying the topology comes before arithmetic.

Which power formula should I use?

Choose the form that matches the known quantities and the constraint. At fixed voltage across a resistor, P = V²/R means increasing R reduces power. At fixed current through it, P = I²R means increasing R raises power.

Example: A 6 Ω resistor connected directly across an ideal 12 V source draws 2 A and dissipates 24 W. Over 30 seconds at that constant power, energy transferred is 720 J.

The phrases “fixed voltage” and “fixed current” are essential. Comparing formulas without those conditions creates an apparent contradiction where there is none.

What changes when a cell has internal resistance?

For a cell delivering current through a simple series circuit, I = emf/(R + r), where R is external resistance and r is internal resistance. Its terminal voltage is emf − Ir.

Example: A cell has emf 6 V and internal resistance 1 Ω, connected to an external 5 Ω resistor. Current is 6/(5 + 1) = 1 A. Terminal voltage is 6 − 1 × 1 = 5 V, also equal to IR across the external resistor.

This discharging-cell relation should not be applied blindly to a charging cell or a more complex network. State the current direction and circuit model first.

How can I check my understanding?

Try these original questions before reading the answers:

1. Two 4 Ω resistors are in parallel. What is their equivalent resistance?
2. The voltage across a fixed ohmic resistor doubles. What happens to its power?
3. A uniform wire's length doubles while its area, material and temperature stay the same. What happens to resistance?

Answers: 1. 2 Ω. 2. Power becomes four times as large. 3. Resistance doubles. If the wire is stretched so its area also changes, the third answer no longer follows from length alone.

Review the assumption behind any answer you missed. Then attempt fresh questions rather than repeatedly recalling these results.

Current Electricity FAQs

Is V = IR valid for every component?

No. A constant-resistance model applies to an ohmic element under suitable conditions. A component with a nonlinear current-voltage characteristic needs its own relation.

Can every resistor network be reduced using series and parallel formulas?

No. Networks with bridges or additional branches may require Kirchhoff's laws. Check node connections before combining resistors.

Is this a complete chapter formula sheet?

No. It covers a core set of relationships and their use. Follow the official syllabus for your exam year and your textbook for the full scope.

Continue with the Physics preparation guide, explore Current Electricity, or take a free PCM paper.