Answer to Question #196025 in Electric Circuits for Asahi

Question

Your car’s 59-W headlight and 25-kW starter are ordinarily connected in parallel in a 16-V system. What power would one headlight and the starter consume if connected in series to a 16-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.)

answer to 2 decimal places.

Answer 1

Power consumed by headlight, $P_1=59\space W$

As it is connected parallel with 16V system

Therefore potential difference across headlight and starter will be same

$V=16\space V$

Resistance offered by headlight, $R_1=\dfrac{V^2}{P_1}=4.33\space \Omega$

Power consumed by starter, $P_2=25\times10^3\space W$

Resistance offered by headlight, $R_2=\dfrac{V^2}{P_2}=0.01024\space \Omega$

Total resistance offered when both the devices are connected in series

$R_{total}=R_1+R_2=4.34024\space \Omega$

Current in the circuit, $I_{total}=\dfrac{16}{R_{total}}=3.686\space A$

Power consumed by headlight, $P_1'=I_{total}^2R_1=58.84\space W$

Power consumed by starter, $P_2'=I^2_{total}R_2=0.139\space W$

Total power consumed in series, $P_{total}=P_1'+P_2'=58.97\space W$