Practice question
Question
A circuit has a \( 9 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and two
resistors \( 5 \, \Omega \) and \( 3 \, \Omega \) in parallel. What is the total current?
Explanation
**Total voltage drop** across series equals source voltage because loop rule Σ V = ε, with internal resistance r included V = ε - I r. For 4 Ω,8 Ω,16 Ω parallel, 1/R_p =1/4+1/8+1/16=7/16, R_p=16/7≈2.29 Ω, then total resistance with internal 3 Ω is 5.29 Ω, current I=18/5.29≈3.4 A. Parallel resistance: (1/R_p) = (1/5) + (1/3) = (3 + 5/15) = (8/15) ⇒ R_p = (15/8) = 1.875 Ω . Total resistance: Rtₒtₐl = 1 + 1.875 = 2.875 Ω . Current: I = (ε/Rtₒtₐl) = (9/2.875) ≈ 3.13 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT],
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