a parallel combination of two resistors of 2ohm each has third resistor of 4ohm in series with the combination.if a battery of 10V with negligible internal resistance be applies across them,find the p.d. across the resistor.
Two 2 ohm resistors in parallel act like a single 1 ohm resistor in series. Total circuit resistance, seen by the battery, is
4 + 1 = 5 ohms.
80% of the p.d. of the circuit is across the 4 ohm resistor.
80% of 10V = ?
Given: E = 10V., R1 = 2 ohms, R2 = 2 ohms, R3 = 4 ohms.
Rt = (2*2)/(2+2) + 4 = 1 + 4 = 5 ohms.
I = E/Rt = 10/5 = 2A.
V3 = I*R3 = 2 * 4 = 8V.
V1 = V2 = E-V3 = 10-8 = 2V.
To find the potential difference (p.d.) across the resistor in this circuit, we need to first calculate the total resistance of the parallel combination of the two resistors and the third resistor in series. Then, we can use Ohm's Law to find the p.d.
Let's break down the problem step by step:
Step 1: Calculate the total resistance of the parallel combination.
When resistors are connected in parallel, the total resistance (Rt) can be calculated using the formula:
1/Rt = 1/R1 + 1/R2 + ...
In this case, we have two resistors of 2 ohms each, so the total resistance of the parallel combination is:
1/Rt = 1/2 + 1/2
1/Rt = 1 + 1
1/Rt = 2
Rt = 1/2
Rt = 1 ohm
Step 2: Calculate the total resistance of the series combination.
When resistors are connected in series, the total resistance is simply the sum of the individual resistances. In this case, we have the third resistor of 4 ohms in series with the parallel combination.
Therefore, the total resistance of the series combination is:
Rs = Rt + R3
Rs = 1 + 4
Rs = 5 ohms
Step 3: Use Ohm's Law to find the p.d.
Ohm's Law states that the potential difference (V) across a resistor is equal to the product of the current (I) flowing through it and the resistance (R):
V = I * R
In this case, we have a battery of 10V (Voltage) with negligible internal resistance. Therefore, the total p.d. (V) across the resistor will be equal to 10V.
As we have already calculated the total resistance (Rs) as 5 ohms, we can rearrange Ohm's Law to find the current flowing through the circuit:
I = V / Rs
I = 10 / 5
I = 2 Amps
Finally, we can find the p.d. (Vd) across the resistor using Ohm's Law:
Vd = I * R3
Vd = 2 * 4
Vd = 8V
Therefore, the potential difference across the resistor is 8 volts (V).