Practice question
Question
A circuit has a \( 12 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and two
resistors \( 2 \, \Omega \) and \( 6 \, \Omega \) in parallel. What is the total current?
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. Parallel resistance: (1/R_p) = (1/2) + (1/6) = (3 + 1/6) = (4/6) = (2/3) ⇒ R_p = (3/2) = 1.5 Ω . Total resistance: Rtₒtₐl = 1 + 1.5 = 2.5 Ω . Current: I = (ε/Rtₒtₐl) = (12/2.5) = 4.8 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's
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