A standard cell has an emf of . If the resistance of the circuit is increasing at the rate of , at what rate is the current changing at the instant when the resistance is ? Assume Ohm's Law .

Question

A standard cell has an emf  of  . If the resistance  of the circuit is increasing at the rate of    , at what rate is the current  changing at the instant when the resistance is  ? Assume Ohm's Law  .

Rheanna · Accepted Answer

First, we denote the following differentiated quantity with respect to time as for simplicity.
 
By differentiating Ohm's Law, we result to the following expression: 
  
 
We know that at the instant, the electromotive force will be constant, and so the rate will be zero.
The current being discharged is     
 
By plugging in the values to the equation, we have:
  
Therefore, the rate of current changing at that instant is .

A standard cell has an emf of . If the resistance of the circuit is increasing at the rate of , at what rate is the current changing at the instant when the resistance is ? Assume Ohm's Law .

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