Analysis of a DC Circuit with Cells, Resistors, and a Diode
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(c) Fig. 8.2 shows a circuit.
The three cells are identical and have zero resistance.
The resistors $R_1$, $R_2$ and $R_3$ are identical.
The reading on the voltmeter is $6.0\text{ V}$.
When the diode is conducting, it has zero resistance and zero potential difference (p.d.) across it.
(i) Determine the e.m.f. of one cell.
$$\text{e.m.f.} = ..............................$$
(ii) Determine the ratio of the p.d. across $R_2$ to the p.d. across $R_3$.
$..................................................................................$
(iii) All the cells are reversed.
1. State and explain the change in current in $R_1$.
$..................................................................................$
2. Determine the new value of the ratio of the p.d. across $R_2$ to the p.d. across $R_3$.
$..................................................................................$
This question includes visual content: A circuit diagram (Fig. 8.2) featuring three identical cells connected in series at the top, with a voltmeter connected in parallel across the entire battery. Below the battery, the circuit branches. The first branch contains a resistor $R_3$ in series with the rest of the network. Following $R_3$, the circuit splits into two parallel branches: one containing a resistor $R_1$ in series with a diode (pointing to the right), and another containing a resistor $R_2$. All resistors $R_1$, $R_2$, and $R_3$ are identical. A handwritten note 'all plus' with an arrow points to the battery, and '3' is written near $R_3$.
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Step by Step Written Solution
Hi Adham, let's look at this circuit problem involving cells in series, resistors, and a diode. First, let's analyze the initial setup of the circuit.
Circuit Analysis
We are given that three identical cells are connected in series. The voltmeter across the three cells reads six volts. Since they are in series, the total electromotive force is the sum of the individual ones.
Since the cells are identical, each cell must have an electromotive force of six divided by three, which equals two volts.
Now for part two, let's determine the ratio of the potential difference across resistor R two to the potential difference across R three. Notice that the diode is forward biased initially.
Ratio of Potential Differences (Initial Case)
In this state, the diode has zero resistance. Therefore, R one and R two are in parallel. Let's call the resistance of each resistor R.
This parallel combination of R one and R two is in series with R three. The potential difference across the parallel circuit is the same as the potential difference across R two.
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