Describe how you would go about proving experimentally that heat produced by an electric current through a resistor is proportional to the square of the current through the resistor
Answers
Answer:
Introduction:-
The power P absorbed in an electrical resistor of resistance R, current I, and voltage V is given by P = I2
R = V2
/R = VI. Despite the fact that it has units of power, it is commonly referred to asjoule heat. A given amount of electrical energy absorbed in the resistor (in units of joules)
produces a fixed amount of heat (in units of calories). The constant ratio between the two has the
value 4.184 J/cal and is numerically equivalent to the specific heat capacity of water. In this lab,
an electric coil will be immersed in water in a calorimeter, and a known amount of electrical
energy will be input to the coil. Measurements of the heat produced will be used to accomplish
the following objectives:
1. Demonstrate that the rise in temperature of the system is proportional to the electrical energy
input.
2. Determination of an experimental value for J and comparison of that value with the known
value.
Theory:
When a resistor of resistance R has a current I at voltage V, the power absorbed in the resistor is
P = I2
R = V2
/R = VI (1)
Power is energy per unit time, and if the power is constant, the energy U delivered in time t is
given by:
U = Pt (2)
Substituting equation 1 into equation 2 gives the following expression for the electrical energy:
U = VIt (3)
When a resistor absorbs electrical energy, it dissipates this energy in the form of heat Q. If the
resistor is placed in the calorimeter, the amount of heat produced can be measured when it is
absorbed in the calorimeter. Consider the experimental arrangement shown in Figure 5.1, which
a resistor coil (also called and “immersion heater”) is immersed in the water in a calorimeter.
The heat Q produced in the resister is absorbed by the water, calorimeter cup, and the resistor
coil itself. This heat Q produces a rise in temperature ΔT. The heat Q is related to ΔT. The heat Q is related to ΔT by:
Q = (mwcw + mccc + mrcr) ΔT The mc’s are the masses and specific heats of the water, the calorimeter, and the resistor. Let mc
stand for the sum of the product of the mass and the specific heat for the three objects that absorb
the heat. In those terms the heat Q is given by the following:
Q = mcΔT (5)
The electrical energy absorbed in the resistor is completely converted to heat. The equality of
those two energies is expressed as
U (J) = J (J/cal) Q (cal) (6)
J represents the conversion factor from joules to calories. Using the expression for U and Q from
equations 3 and 5 in equation 6 leads to
VIt(J) = J(J/cal) mcΔT(cal)
Suppose that a fixed current and voltage are applied to the resistor in a calorimeter, and the
temperature rise ΔT is measured as a measured as a function of the time t. Equation 7 predicts
that a graph with VIt(J) as the y-axis and mcΔT(cal) as the x-axis should produce a straight line
with J as the slope.Equipment:
I
.
Calculations:
Calculate the quantity mc, where mc = mwcw + mccc and record it in the Calculations Table.
Calculate the temperature rise of ΔT above the initial temperature Ti from ΔT = T – Ti for each
of the measured values of T and record the results in the Calculations Table.
Calculate the quantity mcΔT for each case and record the results in the Calculations table.
For each measurement of the voltage V and current I calculate the product VI and record the results in the Calculations Table.