Question

In Figure (a), a R = 49 resistor is connected to a battery. Figure (b) shows the increase of thermal energy Eth in the resistor as a function of time t. The vertical scale is set by Eth =2.50 mJ, and the horizontal scale is set by ts= 4.0s. What is the electric potential across the battery?

Answer 1

First find the power absorbed by the resistor. Remember that power is:

Energy/time.

Since this is a linear graph, we can pick any two arbitrary points and we'll get the same power which will be the slope in this case. It'sconvenient to pick:

(0, 0) and (4, 2.50)

I'll first convert milijoules to Joules: 2.50 mJ = 0.0025 J.

The power of the resistor is:

0.000625 Watts.

The power in a resistor has many form such as:

P = VI = I²R = V²/R.

The last one is the one that will suit us best:

0.000625 = V²/49

V²= 49*0.000625 =0.030625

Answer 2

First find the power absorbed by the resistor. Remember that power is:

Energy/time.

Since this is a linear graph, we can pick any two arbitrary points and we'll get the same power which will be the slope in this case. It'sconvenient to pick:

(0, 0) and (5, 2.50)

2.50/5 = 0.5mJ/s

The power of the resistor is:

0.5mJ/s.

The power in a resistor has many form such as:

P = VI = I2R = V2/R.

The last one is the one that will suit us best:

(0.5*10^-3) = V2/49

V2= 49*(0.5*10^-3) = (2.45e-2)V

Convert to millivolts by dividing by (10^-3)