The formula above is Ohm’s law for an electric circuit with current I , in amperes, potential difference V ,

Question

The formula above is Ohm&rsquo;s law for an electric circuit with current I , in amperes, potential difference V , in volts, and resistance R , in ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by n six-volt batteries that produce a total potential difference of volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, n , of six-volt batteries that can be used?

Accepted Answer

The correct answer is 20. For the given circuit, the resistance R is 500 ohms, and the total potential difference V generated by n batteries is volts. It&rsquo;s also given that the circuit is to have a current of no more than 0.25 ampere, which can be expressed as . Since Ohm&rsquo;s law says that , the given values for V and R can be substituted for I in this inequality, which yields . Multiplying both sides of this inequality by 500 yields , and dividing both sides of this inequality by 6 yields . Since the number of batteries must be a whole number less than 20.833, the greatest number of batteries that can be used in this circuit is 20.

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