Question

Consider the following circuit of three resistors (R1, R2, and R3), with batteries that have emfs ℰ1 = 23. 5 V and ℰ2 = 42 V, and internal resistances r1 and r2.

Find the current I1, in amps.

Find the current I2, in amps.

Find the current I3, in amps

Answer 1

To find the current in each resistor, we can use Ohm's Law and Kirchhoff's laws for circuits.

Step-by-step explanation:

To find the current in each resistor, we can use Ohm's Law and Kirchhoff's laws for circuits. First, let's find the current I1 through resistor R1. Since R1 is in series with the battery ℰ1, the current through R1 will be the same as the current through ℰ1. Using Ohm's Law: I1 = ℰ1 / (R1 + r1).

To find the current I2 through resistor R2, we need to consider the currents at the junctions. At the junction between ℰ1 and R1, the current splits into I1 and I2. Using Kirchhoff's current law, we have I1 = I2 + I3. Rearranging this equation, we can express I2 as I2 = I1 - I3.

Similarly, to find the current I3 through resistor R3, we can set up an equation using the currents at the junction between R3 and R2. By applying Kirchhoff's current law, we have I2 = I3.