9.1 Learners investigated the relationship between potential difference (V) and current (I) for the combination of two resistors, R_1 and R_2 - NSC Physical Sciences - Question 9 - 2017 - Paper 1

The gradient (or slope) of the V-I graph represents the resistance of the circuit in ohms (Ω).

The gradient can be calculated using the formula:

ext{Gradient} = rac{ riangle V}{ riangle I}

From graph X, if the change in potential difference (V) is 2V and the change in current (I) is 0.5A, then:

ext{Gradient} = rac{2V}{0.5A} = 4 ext{ Ω}

Given that the formula for two resistors in series is: $R_{total} = R_1 + R_2$ If we have a gradient of 4 Ω from graph X, we assume this is the total resistance for R_1 and R_2 in series:

Let R_2 be known. Assuming R_1 is the unknown:

Thus, Rearranging the equation gives: $R_1 = R_{total} - R_2$ Substituting the known values can help find R_1.

Using Ohm's law, we can determine the current (I) using the formula:

$I = \frac{V}{R}$ where V = 5V and R = 6Ω. Thus:

$I = \frac{5V}{6Ω} = 0.83A$

For the total emf in the circuit, we can utilize the effective resistance and the current it delivers:

$E = I(R_{M} + R_{N} + r_{internal})$ Substituting the previously found values gives:

$E = (0.83)(1.5 + 0.9) = approximately 6.97V$

The resistance of N can be determined from the circuit analysis. Given that the voltage across M is half of the total voltage, the resistance of N must equal that of M, hence:

The resistance of N is equal to 3Ω.