Physics · Current Electricity · NEET
No. Adding EMFs (E1 + E2) is the rule for cells in SERIES, not parallel. In parallel the EMF does not add up. It becomes a weighted average E_eq = (E1·r2 + E2·r1)/(r1 + r2). If both cells have the same EMF E, then E_eq = E (unchanged). Parallel gives you more current, not more voltage.
Because 1/r_eq = 1/r1 + 1/r2, so r_eq = (r1·r2)/(r1 + r2), which is always less than either r1 or r2. This is the same math as two resistors in parallel. Physically, the current now has two paths (two cells) to flow through, so the total opposition drops. That is the main benefit of parallel cells: lower internal resistance means the battery can supply more current.
Put E1 = E2 = E and r1 = r2 = r. Then E_eq = (E·r + E·r)/(r + r) = 2Er/2r = E. And r_eq = r/2. So n identical cells in parallel give the SAME EMF E but internal resistance r/n. NEET loves this clean case: EMF stays E, internal resistance drops to r/n.
Look at the formula E_eq = (E1·r2 + E2·r1)/(r1 + r2). Each EMF is weighted by the OTHER cell's resistance. So the cell with the smaller internal resistance dominates the result — E_eq is pulled toward it. A strong cell (small r) has more say in the combined EMF.
Then that cell is reversed and its EMF enters with a minus sign (replace E2 with -E2 in the formula). NCERT states this directly. Always check the terminal connections before plugging into the formula, or you will get the sign wrong.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
E_eq = (E1·r2 + E2·r1)/(r1 + r2), where E1, E2 are the EMFs and r1, r2 are the internal resistances of the two cells joined in parallel.
They combine like resistors in parallel: 1/r_eq = 1/r1 + 1/r2, so r_eq = (r1·r2)/(r1 + r2). It is always smaller than either individual internal resistance.
E_eq = E (the same as one cell) and r_eq = r/n. The voltage is unchanged but the internal resistance drops by a factor of n, so the battery can deliver more current.
Parallel lowers the internal resistance and lets the battery supply a larger current without dropping much voltage. Series is used when you need a higher total EMF (voltage).
Yes. NCERT starts from I = I1 + I2 (junction rule) and V = E1 - I1·r1 = E2 - I2·r2, then eliminates I1 and I2 to get E_eq and r_eq. It is a direct application of the junction rule.
