9.1 Define power in an electric circuit - NSC Technical Sciences - Question 9 - 2021 - Paper 1

To calculate the resistance $R$ of the heater element, we can use the power formula:

P = rac{V^2}{R}

Rearranging this gives:

R = rac{V^2}{P}

Substituting the given values:

R = 806.67 \, \Omega$$ Thus, the resistance of the heater element is approximately 806.67 Ω.

First, we need to find the total resistance in the circuit. The total resistance $R_T$ of resistors in series is:

$R_T = R_1 + R_2 = 3 \, \Omega + 5 \, \Omega = 8 \, \Omega$

Using Ohm's Law, we can find the current $I$ in the circuit. The total voltage from the cells is:

$V_{total} = 1.5 \, V + 1.5 \, V = 3 \, V$

Now we calculate the current:

I = rac{V_{total}}{R_T} = \frac{3}{8} = 0.375 \, A

Now to find the potential difference across the 5 Ω resistor:

Using Ohm's Law again:

$V = I imes R = 0.375 imes 5 = 1.875 \, V$

Thus, the potential difference across the 5 Ω resistor is 1.875 V.