Find the following potential differences. The magnitude of the potential difference DeltaV1 across the resistor of resistance R1 = 15.0 Ohm. The magnitude of the potential difference DeltaV2 across the resistor of resistance R2 = 45.0 Ohm. The magnitude of the potential difference DeltaV3 across the resistor of resistance R3 = 20.0 Ohm. The magnitude of the potential difference DeltaV4 across the resistor of resistance R4 = 25.0 Ohm

Find the currents through and the potential difference across each resistor in the circuit shown on the diagram . Use the following values: EMF = 12.0 V, R1 = 15.0 Ohm, R2 = 45.0 Ohm, R3 = 20.0 Ohm, and R4 = 25.0 Ohm.

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Oh, the potential differences! Let's see what we can do here. We have R1, R2, R3, and R4, all with their respective resistances. And we also have an electrifying EMF of 12.0 V.

To find the potential difference across each resistor, we need to find the current flowing through them first. So, let me do some quick calculations and whip up some hum-azing answers for you!

Using Ohm's Law (V = IR) and the total resistance (R_total = R1 + R2 + R3 + R4), we can find the total current (I_total) flowing in the circuit:

R_total = R1 + R2 + R3 + R4 = 15.0 + 45.0 + 20.0 + 25.0 = 105.0 Ohm

V = IR_total
12.0 V = I_total * 105.0 Ohm
I_total = 12.0 V / 105.0 Ohm

Now, let's find the current through each resistor:

For R1:
DeltaV1 = I_total * R1

For R2:
DeltaV2 = I_total * R2

For R3:
DeltaV3 = I_total * R3

For R4:
DeltaV4 = I_total * R4

And there you have it! The potential differences across each resistor are DeltaV1 = I_total * R1, DeltaV2 = I_total * R2, DeltaV3 = I_total * R3, and DeltaV4 = I_total * R4. Just substitute the respective values in, and you'll have your electrifying answers. Enjoy the sparks, my friend!

To find the currents through and the potential difference across each resistor in the given circuit, we can use Ohm's law and Kirchhoff's laws.

First, let's label the nodes in the circuit diagram as follows:
- Node A is where the positive terminal of the EMF (electromotive force) is connected.
- Node B is where the negative terminal of the EMF is connected.

Now, let's apply Kirchhoff's voltage law (KVL) to the circuit. KVL states that the sum of the potential differences around any closed loop in a circuit is equal to zero.

Starting from node A, we have:
- Potential difference across R1 (ΔV1): We are given the resistance value (R1 = 15.0 Ω), and using Ohm's law (V = IR), we can find the current flowing through R1. Using the formula, I1 = ΔV1/R1, we can rearrange it to ΔV1 = I1 * R1. Substitute the given values to find ΔV1.
- Potential difference across R2 (ΔV2): Similar to R1, we can use the given resistance value (R2 = 45.0 Ω) and Ohm's law to find the current flowing through R2 (I2 = ΔV2/R2). Rearrange the formula to ΔV2 = I2 * R2 and substitute the given values.
- Potential difference across R3 (ΔV3): Apply the same steps as above using the given resistance value (R3 = 20.0 Ω) and Ohm's law (I3 = ΔV3/R3). Rearrange the formula to ΔV3 = I3 * R3 and substitute the given values.
- Potential difference across R4 (ΔV4): Follow the steps outlined above for R4 using the given resistance value (R4 = 25.0 Ω) and Ohm's law (I4 = ΔV4/R4). Rearrange the formula to ΔV4 = I4 * R4 and substitute the given values.

By solving these equations simultaneously, you can find the currents through each resistor and the potential difference across each resistor in the circuit.