Two 9.1 ohms resistors are connected in parallel, as are two 5.9 ohms resistors. These two combinations are then connected in series in a circuit with a 20 V battery.

What is the current in each resistor?
I9.1, I5.9 = A
What is the voltage across each resistor?
V9.1,V5.9 = V

First, what is the equivalent resistance in the circuit:

R= 9.1/2+5.9/2=4.55+2.99=7.54 ohms
What is the circuit current? 20/7.54

what is the current in each resistor (half the circuit current)= 10/7.54

Now figure voltage across each resistor.
V=I*resistanceof resistor

To find the current in each resistor, we can use Ohm's Law, which states that the current flowing through a resistor is equal to the voltage across the resistor divided by the resistance.

1. Start by calculating the equivalent resistance of the parallel combination of two 9.1 ohms resistors:
- The formula to calculate the equivalent resistance for resistors connected in parallel is: 1/Req = 1/R1 + 1/R2.
- Substituting the values, we get 1/Req = 1/9.1 + 1/9.1.
- Simplifying this equation, we get 1/Req = 2/9.1.
- Taking the reciprocal of both sides, we find that Req = 9.1/2.
- So, the equivalent resistance of the two 9.1 ohms resistors is 4.55 ohms.

2. Similarly, calculate the equivalent resistance of the parallel combination of two 5.9 ohms resistors:
- Using the same formula, 1/Req = 1/R1 + 1/R2, we find 1/Req = 1/5.9 + 1/5.9.
- This simplifies to 1/Req = 2/5.9.
- Inverting both sides gives us Req = 5.9/2.
- Therefore, the equivalent resistance of the two 5.9 ohms resistors is 2.95 ohms.

3. Now, we have two resistors in series with these equivalent resistances.
- To find the total resistance (Rt) in the circuit, we add the individual resistances: Rt = Req1 + Req2.
- Substituting the values, we get Rt = 4.55 + 2.95 = 7.5 ohms.

4. Use Ohm's Law to find the total current (It) in the circuit:
- Ohm's Law states that It = V / Rt, where V is the voltage and Rt is the total resistance.
- Substituting the values, we find It = 20 V / 7.5 ohms = 2.67 A.

5. Since the two combinations are connected in series, the total current flows through both combinations. So, the current in each resistor is equal to the total current:
- I9.1 = It = 2.67 A.
- I5.9 = It = 2.67 A.

6. Finally, the voltage across each resistor can be found using Ohm's Law:
- V9.1 = I9.1 * R9.1 = 2.67 A * 9.1 ohms.
- V5.9 = I5.9 * R5.9 = 2.67 A * 5.9 ohms.

Solving these calculations will give you the specific values for I9.1, I5.9, V9.1, and V5.9.