Three resistors are connected to a 20 V battery as shown. The internal resistance of the battery is negligible.

(a) What is the current through the 15 resistance?
(b)What is the voltage difference across the 20 resistance?

To find the current through the 15 Ω resistance, we can use Ohm's Law, which states that the current flowing through a resistor is equal to the voltage across it divided by its resistance.

(a) The total resistance in the circuit is the sum of the resistances in series: 15 Ω + 10 Ω + 20 Ω = 45 Ω.

Applying Ohm's Law, we have:

I = V/R

Where I is the current, V is the voltage, and R is the resistance.

Since the voltage across the resistors is provided as 20 V, we can substitute the values into the equation:

I = 20 V / 45 Ω

Calculating this expression gives us the value of the current flowing through the 15 Ω resistance.

(b) To find the voltage difference across the 20 Ω resistance, we can use Ohm's Law once again.

Considering that the 20 Ω and 10 Ω resistors are in parallel, we can calculate the equivalent resistance of this branch using the formula:

1/Req = 1/R1 + 1/R2

Where Req is the equivalent resistance, R1 is the resistance of the 20 Ω resistor, and R2 is the resistance of the 10 Ω resistor.

Substituting the values:

1/Req = 1/20 Ω + 1/10 Ω

Once the equivalent resistance is determined, we can use Ohm's Law to calculate the current flowing through that branch:

I = V/Req

Using the voltage provided as 20 V, and the equivalent resistance calculated, we can find the current. Since the resistors are in parallel, the current passing through the 20 Ω resistance is the same as the current flowing through the 10 Ω resistance. Finally, we can use Ohm's Law once again to find the voltage difference across the 20 Ω resistance:

V = I × R

Using the current and the resistance, we can calculate the voltage across the 20 Ω resistance.