Batteries in circuit, terminal voltage

[scholio]

Homework Statement

two batteries are connected as shown, see attached 'drawing.' what is the terminal voltage across each battery

Homework Equations

electric potential V = IR where I is current, R is resistance

I = V_0/R * e^(-t/RC) where t is time, C is capacitance <--RC circuit, discharging (10V batt.)

I = dQ/dt where t is time, Q is charge

I = epsilon/R e^(-t/RC) where epsilon is emf <---RC circuit, charging (5V battery)

The Attempt at a Solution

i am not too sure about how to approach the problem but by looking at the drawing, i am making the assumption that the current follows a counterclockwise path and that the 10V battery is discharging -->doing work on the 5V battery?

is my assumption correct, if not, how should i approach the problem?

help appreciated

 

[alphysicist]

Hi scholio,

There are no capacitors here, so the equations with capacitances do not apply. You only need Ohm's law, but you might want to solve it using Kirchoff's equations.

The current will not be going counterclockwise. If the 10 V battery was the only battery, the current would be going clockwise. If the 5 V battery were the only battery, it would be going counterclockwise. Since they are both there and the 10V battery has a larger voltage, the current is clockwise.

I don't think you need to account for any discharging or charging of the batteries. Just treat this as a normal circuit. Find an expression for the current, then find the potential difference between the terminals of the batteries (which means, for the left battery, the potential difference from the bottom of the resistor to the top of the 10V emf source).

 

[Moetasim]

Your assumption is correct. In this circuit, the 10V battery is discharging and providing energy to the 5V battery. The terminal voltage across each battery can be calculated using the equation V = IR, where V is the voltage, I is the current, and R is the resistance.

Assuming that the resistance in the circuit is negligible, the current will be the same throughout the circuit. Therefore, the terminal voltage across the 10V battery will be 10V and the terminal voltage across the 5V battery will be 5V.

In this circuit, the 10V battery is providing energy to the 5V battery, so the terminal voltage across the 10V battery will be higher than the terminal voltage across the 5V battery. This is due to the fact that the 10V battery has a higher electric potential (emf) than the 5V battery.

To find the exact values for the terminal voltages, you can use the equations you provided in your homework statement. For the 10V battery, you would use the equation I = V_0/R * e^(-t/RC) and for the 5V battery, you would use the equation I = epsilon/R * e^(-t/RC).

I hope this helps! Let me know if you have any other questions.