Question

Compare the heat produced when two identical resistor of resistance R with the potential difference of V for time T are connected in a series combination and parallel combination

Answer 1

We know, H=VIT {V for Voltage, I for current and T for time}.

Now in series connection, total resistance is R+R=2R, thus I will be:

>V/I =2R (equivalent resistance in series)..............(Ohm's Law)

>2IR=V

>I=V/2R

Now in parallel connection, total resistance is (1/R+1/R)-¹=R/2, thus I will be:

>V/I = R/2 (equivalent resistance in parallel)..............(Ohm's Law)

>I=2V/R

Coming back to H=VIT

V is same for both the circuits.

Thus, H (for series) = V*V/2R*T = V²T/2R

Thus, H (for parallel) = V*2V/R*T = 2V²T/R

Taking V²T/R as constant H for series is 1/4th of H for Parallel

Answer 2

Answer:

For series, H = V^2t/2R

For parallel, H = 2V^2t/R

Explanation:

In series,

Req = R1 + R2

       = 2R

By ohm's law, V = IR

            so,  V = I * 2R

                    I  = V/2R

H = VIt

   = V*V/2R*t

   = V^2*t/2R

In parallel,

Req = 1/1/R+1/R

       = 1/2/R

       = R/2

By ohm's law, V = IR

            so,  V = IR/2

                    I  = 2V/R

H = VIt

   = V*2V/R*t

   = 2V^2*t/R