Practice question
Question
A \( 15 \, \text{V} \) battery with negligible internal resistance is connected to a \( 3 \, \Omega \)
and \( 9 \, \Omega \) resistor in series. What is the power dissipated in the \( 9 \, \Omega \)
resistor?
Explanation
**EMF ε** is work done by non-electrostatic forces per unit charge, terminal voltage V = ε - I r, r internal resistance (Ω), I current (A). When external R = r, total resistance 2r, current I = ε/2r, power in external R is I²R = ε²/4r, total power ε²/2r, so half power dissipated externally, half internally. Total resistance: R = 3 + 9 = 12 Ω . Current: I = (V/R) = (15/12) = 1.25 A . Power: P = I² R = (1.25)² × 9 = 1.5625 × 9 = 14.06 W ≈ 14 W . Applying I = n e A v_d, R
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