Two parallel resistors of values 6.0\text{ }\Omega and 12.0\text{ }\Omega are connected to… — JAMB UTME

Two parallel resistors of values $6.0\text{ }\Omega$ and $12.0\text{ }\Omega$ are connected to a DC power source having an open-circuit voltage of $18.0\text{ V}$ and an internal resistance of $1.0\text{ }\Omega$ . What is the terminal potential difference supplied to the circuit?

$14.4\text{ V}$ Cevap
B
$18.0\text{ V}$
C
$3.6\text{ V}$
D
$17.0\text{ V}$

Cevap

The terminal potential difference supplied to the circuit is

14.4\text{ V}

The option stating

14.4\text{ V}

is correct because the parallel combination of

6.0\text{ }\Omega

and

12.0\text{ }\Omega

gives an external equivalent resistance of

4.0\text{ }\Omega

. With an internal resistance of

1.0\text{ }\Omega

, the total circuit resistance is

5.0\text{ }\Omega

, resulting in a total current of

3.6\text{ A}

. The terminal voltage across the load is

3.6\text{ A} \times 4.0\text{ }\Omega = 14.4\text{ V}

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Calculate the equivalent resistance (

R_p

) of the parallel resistors.

R_p = \frac{6.0 \times 12.0}{6.0 + 12.0} = \frac{72.0}{18.0} = 4.0\text{ }\Omega

Resistors connected in parallel combine according to

\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}

Determine the total resistance (

R_{\text{total}}

) of the entire circuit, including internal resistance.

R_{\text{total}} = R_p + r = 4.0\text{ }\Omega + 1.0\text{ }\Omega = 5.0\text{ }\Omega

The internal resistance of the power source is in series with the external parallel load.

Calculate the total current (

I

) drawn from the power source.

I = \frac{E}{R_{\text{total}}} = \frac{18.0\text{ V}}{5.0\text{ }\Omega} = 3.6\text{ A}

Ohm's law for a complete circuit relates e.m.f., total resistance, and total current.

Calculate the terminal potential difference (

V

V = I \cdot R_p = 3.6\text{ A} \times 4.0\text{ }\Omega = 14.4\text{ V}

(or

V = E - I r = 18.0\text{ V} - 3.6\text{ V} = 14.4\text{ V}

)

Terminal voltage is the voltage across the external load or the e.m.f. minus the lost volts inside the cell.

Anahtar Kavram

Terminal Potential Difference and Internal Resistance

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Cevap

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