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Class XII · Current Electricity: EMF, internal resistance, R_eq.

Topology

Source

EMF ε12.0 V

Internal r0.50 Ω

Resistors

R110.0 Ω

R220.0 Ω

R315.0 Ω

R430.0 Ω

Live readouts

R_eq (external)75.00 Ω

I (battery)0.159 A

V_terminal11.921 V

P_total1.907 W

R1: I, P0.159 A · 0.25 W

R2: I, P0.159 A · 0.51 W

R3: I, P0.159 A · 0.38 W

R4: I, P0.159 A · 0.76 W

Formula

Series:    R_eq = ΣRᵢ           I same in all
Parallel:  1/R_eq = Σ 1/Rᵢ     V same across all
Battery:   I = ε / (R_eq + r)
           V_terminal = ε − I r
Power:     P = I²R = V²/R = VI

Try this: Set all R = 10 Ω, r = 0, ε = 10 V. In series R_eq = 40 Ω → I = 0.25 A. In parallel R_eq = 2.5 Ω → I = 4 A. Same battery: sixteen-fold more current. Now crank r up to 5 Ω and watch the terminal voltage sag.

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