You measure the power delivered by a battery to be 1.15 W when it is connected in series with two equal resistors. How much power will the s

Question

You measure the power delivered by a battery to be 1.15 W when it is connected in series with two equal resistors. How much power will the same battery deliver if the resistors are now connected in parallel across it

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Thiên Ân 5 months 2021-08-26T04:51:10+00:00 1 Answers 3 views 0

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    2021-08-26T04:53:05+00:00

    Answer:

    The power is  P_p  =  4.6 \ W

    Explanation:

    From the question we are told that

       The power delivered is  P_{s} =  1.15 \ W

       Let it resistance be denoted as R

        The resistors are connected in series so the equivalent resistance is  

         R_{eqv} =  R+ R  =  2 R

    Considering when it is connected in series    

    Generally power is mathematically represented as

         P_s =  V * I

    Here I is the current which is mathematically represented as

           I  = \frac{V}{2R}

    The power becomes

         P_s  =  V  *  \frac{V}{2R}

         P_s  =  \frac{V^2}{2R}

    substituting value

        1.15  =  \frac{V^2}{2R}

    Considering when resistance is connected in parallel

      The equivalent resistance becomes

        R_{eqv} =  \frac{R}{2}

    So The current  becomes

           I =  \frac{V}{\frac{R}{2} }  =  \frac{2V}{R}

    And the power becomes

         P_p  =  V  *  \frac{2V}{R}  = \frac{2V^2}{R} = \frac{4 V^2}{2 R} =  4 * P_s

     substituting values

         P_p  =  4 * 1.15

         P_p  =  4.6 \ W

         

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