Question

6. A 1500 MΩ resistor is placed across the terminals of a battery, and a terminal voltage of 2.50 V is measured. When this resistor is replaced with a 5.00 Ω resistor, the terminal voltage decreases to 1.75 V. Find the terminal voltage when a 7.00 Ω resistor is used. (1 point)

Answer 1

Answer:

The terminal voltage is 1.916 V.

Explanation:

Given that,

Resistance = 1500 MΩ

Voltage V= 2.50 V

Decrease voltage V' = 1.75 V

Here, The resistance is very high so the current will be zero in the terminal.

So, the potential difference will be equal to the emf.

$V=2.50 = emf$

Let the internal resistance is r ohm.

We need to calculate the potential difference across internal resistance

Using formula of for potential difference

$V_{r}=V-V'$

Put the value into the formula

$V_{r}=2.50-1.75$

$V_{r}=0.75\ V$

We need to calculate the circuit current

Using formula of current

$i=\dfrac{V}{R}$

Put the value into the formula

$i=\dfrac{1.75}{5.00}$

$i=0.35\ A$

We need to calculate the internal resistance

Using formula of internal resistance

$r=\dfrac{V_{r}}{i}$

Put the value into thew formula

$r=\dfrac{0.75}{0.35}$

$r=2.14\ ohm$

We need to calculate the current

Using formula of current

$i=\dfrac{emf}{r+R}$

Put the value into the formula

$i=\dfrac{2.50}{2.14+7.00}$

$i=0.273\ A$

We need to calculate the potential difference

Using formula of voltage

$V_{r}=ir$

Put the value into the formula

$V_{r}=0.273\times2.14$

$V_{r}=0.584\ V$

We need to calculate the terminal voltage

Using formula of terminal voltage

$\text{terminal voltage}=emf-V_{r}$

Put the value into the formula

$\text{terminal voltage}=2.50-0.584$

$\text{terminal voltage}=1.916\ V$

Hence, The terminal voltage is 1.916 V.