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Anna007 [38]
3 years ago
12

An automobile battery has an emf of 12.6 V and an internal resistance of 0.0600 . The headlights together present equivalent res

istance 5.20 (assumed constant).
(a) What is the potential difference across the headlight bulbs when they are the only load on the battery?
1 V
(b) What is the potential difference across the headlight bulbs when the starter motor is operated, taking an additional 35.0 A from the battery?
Physics
1 answer:
murzikaleks [220]3 years ago
5 0

Answer:

(a) V=11.86\ V

(b) V=9.76\ V

Explanation:

<u>Electric Circuits</u>

Suppose we have a resistive-only electric circuit. The relation between the current I and the voltage V in a resistance R is given by the Ohm's law:

V=R.I

(a) The electromagnetic force of the battery is \varepsilon =12.6\ V and its internal resistance is R_i=0.06\ \Omega. Knowing the equivalent resistance of the headlights is R_e=5.2\ \Omega, we can compute the current of the circuit by using the Kirchhoffs Voltage Law or KVL:

\varepsilon=i.R_i+i.R_e=i.(R_i+R_e)

Solving for i

\displaystyle i=\frac{\varepsilon}{ R_i+R_e}=\frac{12}{0.06+5.2}=2.28\ A

i=2.28\ A

The potential difference across the headlight  bulbs is

V=\varepsilon  -i.R_i=12\ V-2.28\ A\cdot 0.06\ \Omega=11.86\ V

V=11.86\ V

(b) If the starter motor is operated, taking an additional 35 Amp from the battery, then the total load current is 2.28 A + 35 A = 37.28 A. Thus the output voltage of the battery, that is the voltage that the bulbs have is

V=\varepsilon  -i.R_i=12\ V-37.28\ A\cdot 0.06\ \Omega=9.76\ V

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