Question 319: Current Electricity

Question

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P1 , P2  and P3  respectively, then :

Accepted Answer

We have the following cases :
$$\bullet$$ For configuration (I) : Considering as Wheatstone's bridge, we get the equivalent resistance as $${({R_I})_{eq}} = 1\,\Omega $$.
$$\bullet$$ For configuration (II) : The given configuration is further reduced as follows:
That is, $${({R_{II}})_{eq}} = {1 \over 2}\,\Omega $$.
$$\bullet$$ For configuration (III) : Similarly, we get $${({R_{III}})_{eq}} = 2\,\Omega $$.
The power is given by
$$P = {{{V^2}} \over R}$$
Since V is the same for all three configurations, we have the power as a quantity indirectly proportional to the resistance :
$$P \propto {1 \over R}$$
From the above three case, we have $${({R_I})_{eq}} = 1\,\Omega ;\,{({R_{II}})_{eq}} = {1 \over 2}\,\Omega ;\,{({R_{III}})_{eq}} = 2\,\Omega $$, which implies that
$${R_{II}} > {R_I} > {R_{III}}$$
Therefore, $${P_2} > {P_2} > {P_3}$$

Answer

P1  >  P2  >  P3

Answer

P1  >  P3  >  P2

Answer

P2  >  P1  >  P3

Answer

P3  >  P2  >  P1

Current Electricity

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P1 , P2 and P3 respectively, then :

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