Cells in Series
For series cells, equivalent emf is the signed sum of emfs and equivalent internal resistance is the sum of internal resistances. Identical aiding cells give nE and nr.
Why this shows up in the exam
Battery packs for larger voltage · Opposing-cell circuits · Comparing series and parallel cell arrangements
Learn the idea
Series cell emfs add algebraically and their internal resistances add. Series cells push the same current through each source. A reversed cell opposes the others, while every internal resistance still consumes voltage according to current.
🧠 Memory hook: Series: emfs add with signs; internal resistances always add.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E_eq = sum s_i E_i — algebraic emf sum with polarity signs
- r_eq = sum r_i — series internal resistance
- I = E_eq/(R+r_eq) — single-loop series battery current
How to approach it
- 1Mark every cell polarity
- 2Traverse for signed emf
- 3Add all loop resistances
Common slip-ups that cost marks
- •Adding opposing emfs as magnitudes
- •Putting internal resistances in parallel
- •Ignoring a reversed cell's resistance
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
More from Current Electricity
Resistivity, Conductivity, and Material Properties
Learn how resistivity and conductivity depend on material, length, area, and how resistance changes with dimensions and temperature.
Series and Parallel Combinations of Resistors
Master the calculation of equivalent resistance, voltage division, and current distribution in series and parallel resistor networks.
Electrical Energy, Power, and Heating Effect
Calculate electrical energy, power dissipation, and understand the heating effect of current in various circuit configurations.
EMF, Internal Resistance, and Terminal Voltage
Understand the concepts of EMF, internal resistance of cells, and how terminal voltage is affected in real circuits.
Drift Velocity and Microscopic View of Current
Explore the microscopic origin of current, including drift velocity, relaxation time, current density, and the effect of electric field in conductors.
Kirchhoff's Laws and Circuit Analysis
Apply Kirchhoff's current and voltage laws to analyze complex circuits and solve for unknowns.