Practice question
Question
Two cells in parallel have emf \( 12 \, \text{V} \) and \( 3 \, \text{V} \) with internal resistances
\( 4 \, \Omega \) and \( 1 \, \Omega \). What is the equivalent emf?
Explanation
**Internal resistance** causes voltage drop I r inside battery, so V = ε - I r decreases with I. For 16 V battery, r=2 Ω, I=2 A, V=16-4=12 V, external R = V/I =6 Ω. Measurement of V and I yields r = (ε - V)/I. For parallel: εₑq = (ε₁ r₂ + ε₂ r₁/r₁ + r₂) . Substitute: εₑq = (12 × 1 + 3 × 4/4 + 1) = (12 + 12/5) = (24/5) = 4.8 V . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r
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