A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in °C/min) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300kcal/kg·°C, assuming no heat escapes?
Ohm's law
Ohm’s law is a prominent concept in physics and electronics. It gives the relation between the current and the voltage. It is used to analyze and construct electrical circuits. Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it.
Path of Least Resistance
In a series of alternate pathways, the direction of least resistance is the actual or metaphorical route that offers the least resistance to forwarding motion by a given individual or body.
25) A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in °C/min) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300kcal/kg·°C, assuming no heat escapes?
Please show all work using this. (Actual values, equations, and drawings)
![### Educational Transcription of the Handwritten Notes
#### Given Values:
1. \( V_{\text{ab}} = 12 \, \text{V} \)
2. \( \mathcal{E} = 16 \, \text{V} \)
3. \( I = 10 \, \text{A} \)
### Questions:
a) Find \( R \)
b) Find \( P_B \)
c) Given:
- \( m = 20 \, \text{hp} \)
- \( C = 0.2 \, \text{kcal/}^\circ \text{C} \)
Find:
\[ R = \frac{\Delta T}{\Delta t} \]
### Solution:
**a) Calculation of \( R \):**
1. \( \Delta V_{ab} : = \mathcal{E} - I \cdot R \)
2. From ohm's law: \( I \cdot R = \mathcal{E} - \Delta V_{ab} \)
3. Rearrange for \( R \):
\[
R = \frac{\mathcal{E} - \Delta V_{ab}}{I}
\]
4. Substitute values:
\[
R = \frac{16\, \text{V} - 12 \, \text{V}}{10 \, \text{A}} = 0.4 \, \Omega
\]
**b) Calculation of \( P_B \):**
1. Power \( P_B \) is given by:
\[
P_B = I^2 \cdot R
\]
2. Alternatively, it can also be calculated using:
\[
P_B = I \cdot (\mathcal{E} - \Delta V_{ab})
\]
3. Substitute values:
\[
P_B = 40 \, \text{W}
\]
**c) Relationship involving \( R \):**
1. Define \( B = \frac{dE}{dt} \)
2. \( P_B = \frac{\Delta Q}{\Delta t} \)
3. Relating the variables:
- \(\Delta E = \Delta Q = m \cdot C \cdot \Delta T\)
4. Rearranging for resistance \( R \):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F183a4de2-60b8-4988-9fb9-0a70f8d6fd02%2Fd3576f6d-fdde-4b73-a818-6d0b5ff369e3%2Fkyh23q9_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
