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Question

For the circuit shown in the figure, choose the correct options.

A
The value of R1=50 Ω
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B
The value of R=14 Ω
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C
The potential difference across resistor R is equal to 20 V
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D
The current through 10 Ω resistor connected across NP is 0.5 A
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Solution

The correct option is B The value of R=14 ΩThe given circuit can be redrawn as shown in the figure and we can observe that the R1, 10 Ω, 20 Ω resistors are in parallel connection. In parallel the current distributes in inverse ratio of resistance. The current through 20 Ω resistor is 1 A ⇒ Current through 10 Ω connected across P and N will be i=2 A [∵R∝1i for a parallel combination i.e if the resistance is halved hence the current will get doubled and vice-versa.] ⇒R120 Ω=1 A0.5 A Or, R1=40 Ω The net current supplied by battery will be passing through MN, inet=0.5+1+2=3.5 A For the potential difference in circuit we can write, VMN+VNP=69 V ⇒VMN+(i×10)=69 ⇒VMN=69−20=49 V Applying the ohm's law for resistor R, VMN=inetR ⇒R=493.5=14 Ω ∴Option (c) is the correct answer. Tip––––: Whenever the resistors are connected in parallel, always think to apply ohm's law across its end so that we may relate the known current and unknown potential difference in the circuit or the vice-versa.

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